CINCINNATI — With a black glove supporting his left hand, quarterback Carson Palmer went through a full practice on Wednesday, an indication that his sprained thumb won’t be a problem this week.

Palmer hurt the thumb on his nonthrowing hand during the fourth quarter of a 17-14 win over Baltimore on Sunday. He had to hand off using his right hand only for the rest of the game, forcing him to change how he handled the ball.

Palmer said on Wednesday that the thumb was much better — it wasn’t taped when he met with reporters before practice — and shouldn’t affect him on Sunday against the Houston Texans.

The Bengals (4-1) have won three in a row because of last-minute drives led by Palmer, who has been a key reason behind their dramatic rise to first place in the AFC North. They can’t afford to have him hobbled.

‘‘Not an issue at all,’’ Palmer said.

When a teammate lobbed a ball to him during warmups, Palmer fumbled it and dropped it, an indication that he’s still a bit limited. He worked through his limitations in Baltimore after he hit the ground with his left hand after getting hit, hurting the thumb.

For the rest of the game, he made all handoffs with his right hand, which could have created problems. Palmer showed his knack for improvisation: the exchanges with running back Cedric Benson went smoothly.

‘‘I broke my collarbone in college one time and needed to do that for a couple of games,’’ Palmer said. ‘‘I’ve done it before and it’s one of those things you do on the fly.’’

It’s not an issue when he gets ready to throw. Palmer led the Bengals on yet another game-winning drive in Baltimore, completing a 20-yard touchdown pass to Andre Caldwell with 20 seconds left. All five of the Bengals’ games have been decided in the closing minute.

Palmer has led the Bengals on winning drives in each of the last three. He’s been at his best under the most intense pressure, completing 66 percent of his throws for a passer rating of 112.8, which is extraordinary under the circumstances.

Palmer also has kept drives alive by scrambling on third- and fourth-down plays when defenses drop to take away his receivers. Although he’s never been much of a runner, Palmer has become more of a pocket passer since he got his left knee torn up during the Bengals’ playoff loss to Pittsburgh that ended their 2005 season.

The 29-year-old quarterback has been playing the way he did before the reconstructive surgery.

‘‘I was told way back when I had the surgery that it was going to get better year after year,’’ he said. ‘‘I was going to feel 100 percent, but would realize I was 100 percent until the following year and the following year. Body-wise, I feel as good as I felt before I tore up my knee.’’

Palmer didn’t miss a game in the 2006 season even though the knee was still mending. He wore a protective brace and didn’t move around much. By 2007, he was closer to normal physically, but the offensive line was crumbling. Last year, he missed all but four games because of a torn ligament and tendon in his passing elbow. Without Palmer, the Bengals won only four games.

They got a scare in the first preseason game, when Palmer suffered a moderate sprain in his upper left ankle. He missed the last three preseason games and didn’t move around very much during the first couple games in the regular season.

Now, he’s taking off on a scramble whenever the defense forgets about him.

‘‘I think he’s finally getting over the ankle injury,’’ coach Marvin Lewis said. ‘‘It seems less and less bothersome to him that way.’’

Even though he’s feeling better, Palmer would rather not run.

‘‘I’m trying to find a guy open at the last second in those types of situations where the big plays are made,’’ Palmer said. ‘‘Coverages break down after three or four seconds. I’d much rather throw it and get the big-play potential in a throw.’’

NOTES: The Bengals aren’t close to selling out Sunday’s game, which would end their streak of 46 consecutive sellouts at Paul Brown Stadium. The last game that failed to sell out also was against the Texans, on Nov. 9, 2003. … Long snapper Clark Harris looked up at the semicircle of 13 reporters and photographers and laughed. ‘‘You guys will never want to talk to me again,’’ he said. ‘‘That’s what I’m hoping for.’’ The Bengals released snapper Brad St. Louis on Tuesday and signed Harris. Bad snaps were a part of three botched field goals and two botched extra points in the first five games.