Swift scored 20 points and had 12 rebounds to help the Grizzlies beat the Golden State Warriors 100-87 on Saturday night.
Gasol sprained his right ankle near the end of Friday's 107-105 loss at Sacramento after scoring 17 points and matching his career high with 18 rebounds. He finished the game with a slam but left the arena on crutches.
"We don't complain when a guy goes down," Swift said. "We feel like we can fill in for one another. When Pau went down they told me I had to start and all I did was play basketball."
Gasol hurt his ankle when he stepped on Mike Miller's foot with about three minutes left.
"It's kind of sore and doesn't allow me to walk normally," Gasol said. "Hopefully with the day off I will be better and be ready for Monday. Even if I couldn't help the team tonight, every guy here stepped up."
Swift made the biggest difference.
"He moved into Pau's position and did a very nice job," Grizzlies coach Hubie Brown said. "He was extremely instrumental for us in winning this game. He ran Gasol's plays and the opportunities were there."
"The key to the game was getting to the line," Brown said. "We go to the line 42 times and that was big for us."
Troy Murphy scored a career-high 27 points and grabbed 14 rebounds to lead the Warriors, who lost their second in three games. Derek Fisher had 14 points, Jason Richardson added 13 and Speedy Claxton had 10.
"It didn't do us any good," Murphy said. "We're fumbling the ball, throwing to wrong people and turning it over. We have to play harder. I don't know how comfortable you can feel being 2-8."
Warriors guard Mickael Pietrus' season debut lasted about 30 seconds. He entered the game late in the first quarter and was poked in the right eye during a scramble for a loose ball. He was able to return late in the third quarter following treatment. He fouled out after playing 13 minutes.
Pietrus, who separated his left shoulder during a summer game on July 12, came off the injured reserve list earlier in the day.
Memphis took control of the game early and maintained an advantage throughout. Shane Battier hit a 3-pointer from the corner with 10:18 remaining left to give the Grizzlies an 84-66 edge, their largest lead of the game.
"I think we were sleepwalking the whole night," Richardson said. "It felt like we didn't have a lot of energy."
Earl Watson's driving layup gave the Grizzlies a 16-point lead late in the third quarter, and Memphis took a 79-66 lead into the final period.
The Warriors were held to a season-low 67 points when they played in Memphis nine days ago, shooting under 28 percent. They were more efficient this time around but the result was the same.
Memphis never trailed. The Grizzlies opened a nine-point lead and were up 47-42 at halftime.
Warriors center Andris Biedrins was placed on injured reserve with a strained left hamstring, making room for Pietrus. ... Forward Brian Cardinal, who appeared in 76 games with the Warriors last season, received a warm ovation when he entered the game for Memphis. ... The Warriors scored 20 or more points in the first quarter for the fourth straight game after scoring 16 or fewer in
five of their first six games. ... Swift has blocked at least one shot in eight of the first 10 games. ... Grizzlies guard Jason Williams is two assists shy of 3,000 for his career.