Parker was 15 for 21 from the field, putting up a season high while scoring nine of San Antonio's final 10 points in regulation. His 8-footer with 1:01 left in overtime also helped seal a third straight down-to-the-wire Spurs victory, and their eighth straight overall.
Memphis was without the suspended Rudy Gay, but O.J. Mayo (27 points) hit a game-tying 3-pointer with 21 seconds left to force overtime.
In Milwaukee, Utah overcame a double-digit deficit for the ninth time this season and overhauled Milwaukee.
The Jazz shook off a season-low 71 points in their previous game to surge home after falling behind by 12 early.
Deron Williams scored 22 points and added 11 assists, while Al Jefferson added 18 points and nine rebounds for the Jazz, which had 10 of its 14 offensive rebounds in the second half.
Andrew Bogut scored 19 points and had nine rebounds to lead the Bucks.
In Washington, Miami survived a fright from lowly Washington to notch a 12th straight win.
LeBron James had 32 points, seven rebounds and six assists. James and Chris Bosh got away with contact on Kirk Hinrich on a potential game-winning layup, letting the Heat edge the last-place Wizards, who nearly pulled off the upset without injured No. 1 pick John Wall and the just-traded Gilbert Arenas.
Dwyane Wade made a pair of free throws with 7.9 seconds to play to give the Heat their only lead of the fourth quarter. He and Bosh both finished with 20 points.
Nick Young tied his season high with 30 points for the Wizards.
In Orlando, Lou Williams scored 24 points as Philadelphia beat an Orlando team in the midst of a major roster change.
Andre Iguodala had 21 points for the 76ers.
The Magic had only eight players available after two major trades earlier in the day. They acquired troubled guard Gilbert Arenas from Washington, and Hedo Turkoglu and Jason Richardson from Phoenix.
The undermanned Magic managed to keep things close for a half until the Sixers pulled away with a strong second-half defensive push, handing Orlando its sixth loss in seven games.
In Cleveland, Mo Williams scored 23 points, including the tying basket late in regulation and six points in overtime, as Cleveland snapped a 10-game losing streak by beating New York.
Antawn Jamison, who added 21 points, and Anderson Varejao each made two baskets in the extra session as Cleveland broke its longest losing streak since 2002-03.
Amare Stoudemire and Raymond Felton each scored 23 points for the Knicks, who have lost three straight.
In Chicago, Los Angeles stopped Chicago's seven-game winning streak in a thrilling finish.
Chicago guard Derrick Rose, fouled with 0.8 seconds remaining as he drove to the basket, hit the first free throw but missed the second with a chance to tie.
Blake Griffin scored 29 points and Vinny Del Negro made a triumphant return to the United Center as the Clippers recorded back-to-back road wins after having lost their previous 15 away games.
Rose led the Bulls with 34 points.
In Denver, the hosts overcame Kevin Love's career-high 43-point performance in a narrow victory over Minnesota.
Carmelo Anthony scored 24 points and had a key block while Ty Lawson added 23 points to deal the short-handed Timberwolves their 11th straight road loss.
Love also had 17 rebounds for his 14th consecutive double-double. Minnesota was missing two of their top post players, center Darko Milicic and forward Nikola Pekovic, who were both sidelined with sprained ankles.
The Nuggets were without guard Chauncey Billups (wrist) for a third consecutive game.
In Portland, LaMarcus Aldridge had 17 points and 12 rebounds as short-handed Portland held off Golden State.
Monta Ellis, who led the Warriors with 26 points, had a chance to win it but his 20-foot jumper with 0.8 seconds left was off. Golden State has dropped 13 of 15.
Dante Cunningham, making his first start of the season, and Wesley Matthews each added 13 points for Portland, who led by as many as 15 points in the second half before the Warriors rallied.