The third-year player from Marshall broke a bone in his left ankle when he was sacked by Adrian Wilson on his first play of the game, but the Jaguars still won their fourth in a row, 24-17 over the Arizona Cardinals on Sunday.
Leftwich stayed in for four more plays after being sacked before limping off the field and being carted to the locker room for X-rays.
"He's got a crack in the ankle," Jacksonville coach Jack Del Rio said. "The best-case scenario is about a month out, depending on how quickly he heals, and it could be worse. We just won't know until we see how the injury heals."
Garrard, in his fourth NFL season out of East Carolina, had taken just one snap this season before Sunday.
"That's my job to step in when Byron goes down," Garrard said, "and it's happened now, so I've got to step up and do my job and everyone here has my back. I don't feel like I have to have the pressure, going out and winning every game on my own, putting all the games on my shoulder."
Arizona had prepared for Leftwich, a pocket passer with little mobility. Garrard is a scrambler.
"That was a big difference," Cardinals coach Dennis Green said. "It was very difficult to keep him contained and focus on the pass defense aspect of it."
The Jaguars also were without starting running back Fred Taylor because of an ankle injury.
Neil Rackers' string of 31 consecutive field goals, tied for third-longest in NFL history, came to an end on the first series of the windy afternoon when his 43-yard attempt was wide left.
After Arizona's Kurt Warner threw incomplete on fourth-and-1 from the Cardinals 40 with 4:27 to play, and Anquan Boldin was called for unsportsmanlike conduct, Jones scored to put Jacksonville (8-3) ahead 24-10 with 4:20 to play.
An onside kick try failed, but Jacksonville couldn't move the ball and Arizona took over on its 20 with 1:52 to play. Arizona drove to the Jaguars 36, but Warner was hit from behind by Akin Ayodele, fumbled and Jacksonville's Rob Meier recovered, assuring the victory.
Warner completed 29-of-46 passes for 315 yards and two touchdowns, with one interception. In the second half, he was 21-of-31 for 261 yards.
"I thought in the first half defensively, we played well," Del Rio said. "In the second half we weren't quite as sharp, and Kurt Warner got hot and looked like the two-time MVP that he is."
Boldin caught 10 for 115 yards. Garrard was 12-for-26 for 115 yards and rushed for 62 yards in five carries.
"He protected the football, which is the biggest thing, didn't turn it over, made some big runs," Del Rio said.
Garrard finished Jacksonville's 10-play, 67-yard opening drive, running 16 yards on a bootleg to make it 7-0.
The Cardinals cut the lead to 10-3 on Rackers' 42-yard field goal with four minutes left in the third.
It was a nasty game with several personal foul calls, two against Boldin and two against his defender Terry Cousin. Each team drew 11 penalties, Jacksonville for 81 yards and Arizona for 105. Boldin said he was not upset about the penalties he committed and hinted of dirty play by the Jaguars' top-rated pass defense.
"I can't say what I want to say," Boldin said. "But I will say 'You watch the film and tell me what you think about it.'"
After the field goal, Wimbush -- whose previous best return this season was 36 yards -- took the kickoff at the 9 and appeared to be stopped near midfield. He was spun around by would-be tackler Quentin Harris, broke free and ran untouched across the field and to the right corner of the end zone, making it 17-3.
"I just run hard," Wimbush said. "I do what the coaches say. They say 'go north and south with it' and I take it north and south."
- Arizona knocked a starting QB out for the second week in a row. Last week against St. Louis, Marc Bulger was sidelined with a shoulder injury.
- Jacksonville hasn't won four in row since 1997.
- Garrard had two starts last season when Leftwich was out with a knee injury.
- Warner had his 34th career 300-yard passing game and third in his last four starts.