McMurray began his Cup career with Ganassi in 2003, left for Roush Fenway Racing in 2006-2009 and returned to Ganassi's team in 2010.
It was a triumphant return, with McMurray winning the Daytona 500, the Brickyard 400 at Indianapolis Motor Speedway and a race at Charlotte Motor Speedway in that 2010 season. But Ganassi's cars then struggled to consistently keep pace with those of NASCAR's other top teams.
In McMurray's prior 19 starts at Auto Club Speedway, his best finish was fourth, in 2004 and again in 2005. He finished sixth last year.
Other drivers have noticed McMurray's resurgence. "I can see him driving with a new confidence," four-time Cup champion Jeff Gordon said. "I definitely think they have turned the corner and made improvements."
Brian Vickers has been sidelined again by blood clots that will prevent him from racing this weekend.
The driver of the No. 55 Toyota for Michael Waltrip Racing has been placed on blood thinners, and 22-year-old Brett Moffitt was tapped to replace him this weekend, the team said. Moffitt qualified 30th for Sunday's race.
Vickers missed the first two races this season, at Daytona and Atlanta, while recovering from heart surgery last December.
The surgery was to repair an artificial patch over a hole in his heart, a patch first inserted in 2010 amid his first bout with blood-clot problems.
Team co-owner Michael Waltrip drove Vickers' car in the Daytona 500 and finished 26th; Moffitt drove the car at Atlanta Motor Speedway and finished eighth.