Toms and Camilo Villegas both fired a 9-under 63 in a revamped tournament that previously was known as the Bob Hope Classic.
The event was reduced from five rounds to four this year and is being hosted by former President Bill Clinton. Instead of being paired with four different four-member amateur teams during the tourney, each professional now competes alongside the same amateur partner throughout the competition, and three courses are used for the tournament instead of four.
Toms played Thursday at the La Quinta Country Club and Villegas shot his 63 at the PGA West Nicklaus Course.
Toms has won 13 times during a 14-year PGA Tour career, but his victory last season at the Colonial Invitational was his first triumph since 2005.
The traditional low scoring in the Palm Springs area has not changed this year and the co-leaders had a one-shot advantage over Ted Potter, Sang-Moon Bae and Brandt Snedeker.
Phil Mickelson, making his 2012 debut, had a wild round of 74 that included an eagle, three birdies, two bogeys, a double bogey and a triple bogey. Johnson Wagner, who won the year's first full-field event last week in Honolulu, shot a 68.