Glover fired a 7-under 65 at La Quinta, while Rose posted his 70 at The Classic Club.
This is the only five-round tournament on the PGA TOUR schedule. The format saw each player grouped with amateurs over the first four rounds.
John Rollins, who had gotten within one stroke of the lead during round four, posted a 5-under 67 at PGA West. He is alone in third at 18-under-par 270. Jeff Quinney and Charley Hoffman share fourth at minus-16.
Rose got off to a quick start with a birdie at the first. He came right back with a 9-foot birdie putt at two. Rose pushed his lead to five strokes with a birdie at the fifth.
The Englishman stumbled to a bogey on six however. Rose atoned for that mistake with a birdie at the eighth. After getting up and down for par on 10, he pushed his drive right and into water off the 11th tee. Rose, who is looking for his first PGA TOUR win, managed to save bogey, but his lead was down to one as Rollins was making a move.
'Ten and 11 were playing pretty tough today. They're both into the wind and about 460 yards,' Rose stated. 'I got away with an up-and-down par on 10, then hit it in the water on 11, but actually made a great five. I was really happy momentum-wise walking to the 12th tee having gotten through those two holes at 1 over.'
Rose bounced back with a 5-foot birdie putt on 13. He had more tee trouble on the par-5 14th as his drive found the trees left of the fairway and he had to punch out from there.
The 26-year-old reached the green with his third, but three-putted for his third bogey of the round. Rose got that stroke back by draining a 12-foot birdie putt on 15.
Rose three-putted for his fourth bogey of the round at 16, which dropped him to 20 under. He parred his final two holes and was caught by Glover shortly after completing his round.
'A little ragged there on the back nine,' said Rose. 'I three-putted twice coming in and I guess that's what slowed my momentum.'
Rose played The Classic Club on Saturday and will play it again Sunday and hopes that will be beneficial.
'I think it will be an advantage playing this course two days in a row,' he explained. 'Every day everyone's faced with the challenge of getting used to the speed of the greens. I felt I've coped with that well this week. Today was the one day I didn't quite have the pace of the greens. So maybe to come back tomorrow it will be a slight advantage playing this surface two days in a row.'
Glover faltered to a bogey on the 10th at La Quinta, his first hole. He erased that mistake with a birdie at the next. Glover poured in consecutive birdie putts from the 16th to make the turn at 15 under.
The 27-year-old collected his fourth birdie on the round at the second. Glover flew up the leaderboard with three straight birdies from the fourth to get within one of Rose's lead.
Glover, the 2005 FUNAI Classic winner, rolled in a seven-foot birdie putt on eight to move into a tie for first. He two-putted for par from the fringe at the last to share the overnight lead.
'I bogeyed the first, but things turned around from there,' Glover said. 'It was a little slow, but I got going on the front, my back nine, and turned in a good one.'
Vaughn Taylor fired a 7-under 65 at Bermuda Dunes to move into a share of sixth place. He was joined at 15-under-par 273 by Joe Durant, Robert Allenby, Heath Slocum, Duffy Waldorf, Dudley Hart and Matt Kuchar.
Reigning Masters champion Phil Mickelson returned to action for the first time since the Ryder Cup this week. Mickelson carded nine birdies, a bogey and a double-bogey as he shot 6-under 66 to move into a tie for 19th at minus-13.
The cut line fell at 6-under-par 282 with 76 players advancing to the final round. Among those missing the cut were former British Open winner Todd Hamilton (286), 2006 champion Chad Campbell (286), two-time major champion Mark O'Meara (286) and 2002 PGA Championship winner Rich Beem (293).