Kansas (23-5, 13-2 Big 12) led by as many as 21 points in the second half before a big run by the Aggies got them within striking distance.
A 3-pointer by Dash Harris cut the Kansas lead to four points, but Taylor made the first of two free throws to leave Kansas up 61-56 with about a minute remaining.
Johnson added a free throw before Thomas Robinson fouled out on a technical he received during a scuffle between players when they were trying to secure a loose ball.
Elston Turner made both free throws to make it 62-58 with 40 seconds left, but Jeff Withey scored four points after that to guarantee the win.
Khris Middleton led Texas A&M (13-14, 4-11) with 23 points.
The victory is the fifth straight for the Jayhawks whose next game is a showdown for the conference lead with No. 3 Missouri on Saturday.
Kansas led 60-53 after Taylor scored the first basket for Kansas in almost 7 minutes on a three-point play with just under 2 minutes remaining.
Johnson finished two points shy of his career-high and had 18 points in the first half to carry the team with Robinson and Taylor struggling before halftime.
Texas A&M shook off a bad start to the second half by going on a 24-8 run starting at the 11-minute mark to cut the Jayhawks' lead to 57-53 with about 2 minutes remaining. Kansas made six free throws in that span, but the team's only basket came on a layup by Johnson with just under 9 minutes remaining.
Middleton scored 13 points in that time.
The Jayhawks were leading by seven points early in the second half before they scored 14 straight points to stretch the lead to 47-26 with just more than 13 minutes remaining. Robinson had five points in that span and capped the run with a three-point play.
Robinson finished with 10 points and 13 rebounds to extend his streak of scoring in double figures to 16 straight games.
This is the seventh straight season the Jayhawks have had 13 conference wins and their 23rd consecutive season with 23 wins. They have won eight straight over A&M and are 19-1 all-time against the Aggies in what could be the last meeting with A&M heading to the Southeastern Conference next season.Harris, a point guard, missed the last seven games with an injured foot. He didn't start, but entered the game early in the first half in his first game since Jan. 23 at Kansas.
He had eight points and David Loubeau and Turner added 10 points each for the Aggies, who trailed 31-21 at halftime.
TEXAS A&M HEAD COACH BILLY KENNEDY
I'm kind of sorry you had to watch that‐ it was an ugly game. Fortunately both teams were ugly. You can't give Kansas a 20‐point lead on your home court and expect to play perfectly and win the game. The only thing I can say is we didn't throw in the towel. We had some opportunities.
On Khris Middleton's play
He was big for us. We played him at the 4, and it was a mismatch at times. I thought that was key. And defensively we picked up our energy finally when we started to make some shots.
Was the missed three by Kinsley what you wanted on that play near the end of the game?
No, we were trying to drive the ball. We had a small line up in the game and we wanted him to drive the ball or shoot the three, which we think he had an opportunity to make.
On having Dash Harris back
It was good to see Dash back out there. He moved pretty well and played 24 minutes, and down the last stretch. Defensively I thought he did a pretty good job at the top of our defense.
On Elijah Johnson's play
That's the mark of a good team that has talented players. Elijah is a good players. We took a chance to take Robinson away and leave him open‐ but he's a good player ad stepped up and made shots.
On Loubeau fouling out
It was a loss not having him. But I thought Ray Turner defensively did a really good job down the stretch.
SENIOR GUARD DASH HARRIS
What made it tough to play against Kansas' defense?
We just didn't take smart shots, we rushed up, took quick shots that weren't good team looks, and it put us in a hole. We can't play against top‐10 teams or any team playing behind like that.
How do you evaluate your game tonight?
I'm never satisfied with anything. It was just good to be out there tonight with my teammates. I just wanted to wait until I was healthy enough to do some of the things I do best, which is run the floor and play hard defensively. And I think I was able to do some of those things tonight.
On Kansas having big plays, and Tyshawn Taylor's three‐point play late
They had a lot of big plays. That was a big momentum swing for them. It broke our momentum‐ it was a big play. Rebounding the ball, missing free throws, everything is a big play down the stretch.
JUNIOR FORWARD KHRIS MIDDLETON
What were you guys doing during the comeback?
Just playing hard, playing our game and trying to get stops.
What was your role out there tonight?
I was just trying to play my game, get in the zone and play some team basketball and find my teammates. I was just trying to make things happen.
KANSAS HEAD COACH BILL SELF
Was this one of those games where you just can't make shots?
You know I don't know. I thought that we had a couple of key players play miserably the first half and kind of got it going a little in the second half. They played better and we played awful down the stretch.
Was it you playing bad or A&M playing well that sparked A&M's comeback?
I think it's a combination. I think that A&M played pretty good down the stretch. They shot 50 percent in the second half. Middleton got on a roll, Dash got a big three. I think we helped them though.
On the team making bad plays but having a decent end to the game
No, we actually did okay tonight he last couple of minutes considering key players didn't play. The last couple of minutes we didn't play great obviously, we didn't make free throws, but I don't think it was us turning us over, but us making bad plays.
On Thomas Robinson's technical foul
Inexcusable. As bad a play as I've seen.
On Elijah Johnson's play
Elijah was great in the first half. I didn't realize he had 18 until I got to the stat sheet. When your second leading scorer has four, that's obviously not great.
On Tyshawn Taylor's play
He can go get in the paint and get his own shot‐ he needs to start getting more shots for his teammates. But I think he's as good as it gets in the country when it comes to getting your shoulder past people.
SENIOR G TYSHAWN TAYLOR
On Elijah Johnson's first half...
"He was huge. He got us off to a good start and shot the ball well. We had kind of been waiting for him to get going. It was good for him to get a little bit of confidence going into a big game on Saturday."
Is it frustrating that A&M cut your lead down so much?
"For sure. We were up 21 with 14 minutes left in the game and you've got to be able to put teams away when you're up that much. We made the game interesting. It was good that we pulled that out but we shouldn't have let it get that close after we had such a big lead."
What happened to cause the A&M run?
"They went to a match‐up, and Thomas got in foul trouble, he was sitting on the bench. We just weren't hitting shots all night, besides Elijah, he was the only one making some shots. You have to credit their defense-we know they're a good defensive team, they were physical with our bigs and pressuring the ball and stuff like that. We were getting looks but we just weren't hitting them. Khris Middleton played amazing in that second half. He sparked them a little bit. You've got to be able to withstand runs and make your own, and we didn't. They made a huge run and if we hadn't had a 20‐point lead that game could have gone either way."