Murray had 19 points and 10 assists and Poeltl had 18 points with nine rebounds by the end of the third quarter, and neither played after that with the Spurs up by 31.
"We managed to find our rhythm early in the game and it really carried over for the rest of the game," Poeltl said.
Houston led early in the first quarter, but the Spurs soon took over and were up by 15 at halftime. A 39-point third quarter put the game out of reach on a night San Antonio scored a season-high 82 points in the paint and shot a season-best 57.4 percent.
The win comes after the Spurs dropped consecutive games to Brooklyn and Philadelphia at home.
"That was a good response to a loss where we started out poorly," coach Gregg Popovich said. "Tonight we started off aggressively and played a full 48."
San Antonio's 82 points in the paint is tied with the Grizzlies for most in the NBA this season and it's the second-most the Spurs have had since 2000.
"We were a step slow, we were off of our game plan, we were frustrated most of the time because of our mistakes," Houston coach Stephen Silas said. "So, not a good effort from our group."
Kevin Porter Jr. had 16 points and nine assists for the Rockets, who lost their second game overall and ninth in a row at home. Christian Wood scored 15 points with seven rebounds for Houston.
Keldon Johnson added 16 points for San Antonio and Doug McDermott had 15.
Popovich was complimentary of Murray's play on Tuesday.
"He's definitely setting the tone," he said.
San Antonio was up by 15 with about 8 minutes left in the third quarter before using an 8-0 run with all the points in the lane, to extend it to 83-60 two minutes later. Houston had two turnovers in that stretch to help the Spurs pad the lead.
Jae'Sean Tate made Houston's first points in almost 2 minutes on a layup after that, but the Spurs used a 10-3 spurt to make it 93-65 with four minutes left in the third. Murray and Drew Eubanks had four points each to power that run.
The Spurs led 105-74 entering the fourth quarter.
Spurs: Keita Bates-Diop missed the game due to health and safety protocols. ... Eubanks had 13 points and nine rebounds off the bench. ... San Antonio was 6 for 6 on free throws.
Rockets: Houston made just 9 of 34 3-point attempts. ... Alperen Sengun, who had 14 points, received a technical foul in the second quarter. ... Usman Garuba sat out with an injured left wrist. ... Kenyon Martin Jr. had 13 points and eight rebounds off the bench.
Houston rookie Jalen Green, the second overall pick in the draft, continued a recent shooting slump Tuesday. Green made 3 of 16 shots overall and just 1 of 8 3-pointers to finish with seven points.
He is 3 of 32 from 3-point range in the last six games combined. But Silas isn't worried about the 19-year-old because he sees the work he puts in each day to improve.
"He will shake out of it," Silas said. "I'm sure of that."
Spurs: Host Memphis Wednesday night.
Rockets: Host Portland Friday night.
Keldon Johnson with a ferocious dunk
Keldon Johnson throws down an emphatic dunk in the third quarter of the Spurs' dominant win vs. the Rockets.