HOUSTON -- The adversity that championship contenders annually overcome found the Rockets on Saturday night when two missing rotation players, plus a hobbled All-NBA guard, exacerbated the challenge of playing the second game of a back-to-back following a key win.

James Harden disregarded right knee discomfort while Chris Paul found his shot in the second half to finish with a game-high 31 points as Houston extended its NBA-leading winning streak to 13 games with a gritty 115-111 victory against the Milwaukee Bucks at Toyota Center.

Paul had only two points on 0-of-5 shooting before the intermission but opened the second half by drilling three consecutive 3-pointers. He was just as lethal down the stretch, going 4-for-5 in the fourth quarter and nailing back-to-back mid-range jumpers to lift Houston (24-4) to a 111-104 lead with 33.7 seconds left. Paul missed one shot after the break and had 25 points.

Houston improved to 14-0 with Paul in the lineup but had to fight hard to the finish. The Rockets were without starting center Clint Capela and reserve forward Luc Mbah a Moute. Harden played through pain after sustaining his injury Friday against San Antonio. The Bucks (15-13) dropped their third consecutive game but made Houston labor for its victory.

"I'm a big believer in things being mental," Paul said. "This game was tough. They're a grind-out team and they make you guard every time down. Mentally this was a big win for us. We never let go of the rope. Every time they made a little push we stayed right there down the stretch.

"(Heck), James was out there basically on one leg. The mental toughness we showed as a team is what we take from this game."

The Rockets struggled from the perimeter throughout, finishing 11-for-35 on treys. But in the fourth quarter they produced timely 3s, first with Eric Gordon doubling the lead to 87-81 at the 10:43 mark. Harden hit a 3 through a Malcolm Brogdon foul and completed a four-point play with 5:42 left. Trevor Ariza answered an 8-0 Milwaukee run with a corner 3 with 2:24 to play.

Houston attacked the rim, and its persistence paid off in the form of 42 free-throw attempts.

"That's what we do. We have several guys that can do that as well," said Harden, who also had six rebounds and five assists. "Obviously, a lot of guys can shoot, but we've got guys that can put pressure on that rim and bigs that can put pressure on that rim as well. When shots aren't falling we're still able to attack the basket."

The Bucks were relentless. When Paul hit the third of his third-quarter 3s, Houston led 70-59. Milwaukee, led by Giannis Antetokounmpo, Eric Bledsoe and Brogdon, responded with a 14-3 run. Houston led 103-91 after Gordon completed a nifty reverse layup at the 4:18 mark of the fourth only for Khris Middleton and Antetokounmpo to combine for eight straight points.

"On the road, on a back-to-back, we gave ourselves a chance," Bucks coach Jason Kidd said. "We just came up short."

Antetokounmpo paced Milwaukee with 28 points and nine rebounds. Middleton added 23 points, 12 in the fourth. Brogdon scored 20 points off the bench while Bledsoe added 19 points.

Brogdon and Bledsoe combined for 26 points in the first half, taking full advantage of the Rockets' fixation on Antetokounmpo, who attempted only seven shots before the break. The Bucks repeatedly mounted answers to each Houston run, only going silent during a four-minute stretch in the fourth when the Rockets extended their lead to a dozen for the first time.

"I'm happy with the effort," Middleton said. "We gave it our all and we took them to the wire. It just came down to a couple stops again late in the game that somehow we've just got to find a way to get back to that like we were in the beginning of the season."

NOTES: Bucks G/F DeAndre Liggins made his first start of the season, replacing Bucks G Gary Payton II. Payton had started four consecutive games for injury-riddled Milwaukee, averaging 3.3 points over 13.9 minutes in those games. ... Rockets C Clint Capela missed his first game of the season with a left heel contusion. With Capela out, veteran C Nene played in both games of the back-to-back and scored a season-high 16 points Saturday. ... Rockets G Chris Paul recorded one steal and snapped a tie with Kobe Bryant for sole possession of 14th place on the all-time steals list with 1,945.