Los Angeles led by 14 points in the second half, then held on improve to 3-3 since LeBron James was sidelined Nov. 4 because of an abdominal strain. The Lakers have won four overall games this season without James, one a 125-121 overtime victory in San Antonio on Oct. 26.
Davis had the big game two days after the Lakers were humbled by 24 points in a home loss to Minnesota, with the All-Star forward saying afterward the performance was ''embarrassing'' and that the team lacked effort in a deciding third quarter.
His effort Sunday was a concerted effort to lead by example.
''I wanted to come out and dominate the game and do whatever I could to get the team going,'' Davis said. ''That's the type of energy you need from our bench, our star players, our role players.''
Dejounte Murray had a triple-double for the Spurs with 22 points with 10 rebounds and 10 assists. Keldon Johnson scored 24 points. Murray's other triple-double came in the previous meeting against the Lakers.
San Antonio lost for the fifth time in its last seven games and fell in the opener of consecutive games at Los Angeles, with a meeting against the surging Clippers on Tuesday night.
''I was really happy with their effort,'' Spurs coach Gregg Popovich said. ''Too many turnovers tonight against those guys, but we never gave in. They kept playing, they're getting better. They've got to keep their energy up.''
The Spurs gave up 19 points on 15 turnovers, while scoring 15 points on 16 Lakers turnovers.
Davis scored 19 points in the first quarter on 8-of-10 shooting and had 27 points in the half. The return of Horton-Tucker also helped with the early energy level. The third-year player found a comfort zone in the second half with 12 points.
''We have a strong belief in that young man and what he can do on both sides of the ball,'' Lakers head coach Frank Vogel said about Horton-Tucker. ''Obviously, when we get whole, we have a log of good choices, but he's going to be a big part of it.''
The Spurs pulled to 105-103 with 2:41 remaining on a 3-pointer from Doug McDermott. The Lakers had a 7-0 run to take control, getting a 3-pointer from Anthony with 1:46 to go for a 110-103 lead and a layup from Russell Westbrook for a 112-103 edge.
Westbrook finished with 14 points, 11 rebounds and seven assists. Malik Monk had 16 points for the Lakers.
''One day at a time, that's all I can tell you,'' Westbrook said when asked if the Lakers are close to being the team they hoped to be with James' return around the corner. ''We hope so but we'll take it one day at a time and slowly get guys back and get it turned around.''
''They just got to keep their energy up and their belief up that the worm will turn as long as we continue to execute better and better,'' Popovich said.
Spurs: C Jakob Poeltl was eligible to return from COVID-19 protocols but watched from the bench in street clothes as he works on his conditioning. Poeltl ''might be available'' for Tuesday's game against the Clippers, according to Popovich. . F Keita Bates-Diop played three minutes Sunday after missing two games with a lower back bruise.
Lakers: Horton-Tucker (thumb) was in the starting lineup for his season debut and made his first basket on a 3-pointer just under four minutes into the game. . Anthony made his first start of the season after starting three times in 69 games for the Portland Trail Blazers last season. It was his 1,118th career start.
Spurs: At Los Angeles Clippers on Tuesday night.
Lakers: Host Chicago on Monday night.