Verplank fired a 7-under 65 at La Quinta, while Rose was one worse with a 6-under 66 in round two on The Classic Club.
This is the only five-round tournament on the PGA TOUR schedule. The format sees each player grouped with amateurs over the first four rounds before the cut is made.
The golfers compete on all four courses -- Bermuda Dunes Country Club, the Arnold Palmer Private Course at PGA West, La Quinta Country Club and The Classic Club, which will host the final round on Sunday.
First-round leader Robert Allenby managed a 2-under 70 and is tied for third place at minus-11. He was joined there Johnson Wagner (67), a two-time winner on the Nationwide Tour last year. Matt Kuchar and John Rollins are one stroke further back at 10-under-par 134.
Reigning Masters champion Phil Mickelson is playing this week for the first time since the Ryder Cup. He struggled to a 2-under 70 Thursday and is tied for 51st at 4-under-par 140. Mickelson carded three birdies, three bogeys and an eagle in the second round.
Verplank, who shared second here last year, started on the back nine at The Classic Club. He birdied his first hole, then collected his second birdie by sinking a 12-foot putt on the par-4 13th.
The 42-year-old dropped in back-to-back birdies from the 15th to move to 10 under. Around the turn, Verplank birdied the first from 30 feet out to move into share of the lead.
Verplank moved out in front with a two-putt birdie on the par-5 fourth. He came right back with a birdie at the fifth to move to minus-13. After three straight pars, he headed to the 18th with a one-stroke cushion.
After finding the right rough off the tee, Verplank's second shot landed in the water. That led to a closing bogey which dropped him into a share of the lead with Rose.
'I actually had a pretty good second shot at the green. I just hit a bad shot,' admitted Verplank. 'The only thing that made me mad was how I left that 30-foot putt for par about 5 feet short. I was not happy about that.'
Rose got off to a slow start as he was 1 over through four holes. He got on track by holing out from a bunker for eagle at the par-5 fifth.
The Englishman got up and down for birdie on the sixth to get to 7 under. Rose picked up his second birdie on the eighth.
Around the turn, he caught fire. Rose birdied the 10th. After draining a birdie on 11, Rose holed out again from a bunker for birdie on the par-3 12th to get to 11 under.
Rose capped his round with a birdie on the par-4 18th to gain his share of the lead.
'I was obviously very pleased to get in there with a 65,' Rose commented. 'The greens at La Quinta are rolling really well and they are also very fast. So you have to be sort of very careful around the cup today. You could leave yourself 3- or 4-footers which I managed to hole today which kept the score going.
'I was obviously very pleased with the way I played. I holed two bunker shots. Really my short game today was the reason I played so well and scored so well.'
Ted Purdy matched Rose's 65 as the low round of the day. Purdy stands at 9- under-par 135 and it tied for seventh place with Shane Bertsch and Mark Calcavecchia.
Kenny Perry, Tripp Isenhour, Ryan Armour, Daniel Chopra, Joe Durant, Dudley Hart, Charley Hoffman and Heath Slocum are one stroke further back at minus- 8. The cut will occur after the fourth round.