SANTA CLARA, Calif. >> A timely trick play and a big turnover helped the San Francisco 49ers to a second straight win.

Colin Kaepernick threw for 201 yards and a touchdown, Frank Gore ran for 107 yards and the 49ers converted a fake punt to beat the Kansas City Chiefs 22-17 on Sunday.

The 49ers (3-2) turned to a trick play on fourth-and-1 from their own 29 early in the fourth quarter, giving a direct snap to Craig Dahl for a 3-yard run up the middle. Kaepernick directed the offense down field, and Phil Dawson kicked a 27-yard field goal with 8:42 to play for the go-ahead score.

Dawson also connected from 55, 52, 35 and 30 yards.

The 49ers held off former franchise quarterback Alex Smith and the Chiefs (2-3) twice in the closing moments. Smith threw for 175 yards and two touchdowns, but Perrish Cox intercepted his overthrown pass to end any chance Kansas City had to rally.

San Francisco’s win should help quiet all the questions — at least for a week — about whether there’s any rift between coach Jim Harbaugh and the locker room.

Reports have been appearing since the offseason that players weren’t particularly happy with Harbaugh, and the latest round sent 49ers CEO and acting owner Jed York to Twitter to try and silence the chatter Sunday morning.

York posted: “Jim is my coach. We are trying to win a SB, not a personality or popularity contest. Any more questions?”

Harbaugh helped answer them by trusting his team on a big trick play, and he leaned on Kaepernick, Gore and a timely defense to do the rest with tight end Vernon Davis out with a back injury.

San Francisco sparked the offense with the fake punt, and even more big plays followed. Brandon Lloyd made a leaping 29-yard catch over Sean Smith to extend San Francisco’s drive again, helping set up Dawson’s fourth field goal.

Dawson also lined up for a 54-yard field goal with 4:19 remaining after San Francisco stopped Kansas City, but the Chiefs were penalized for having 12 players on the field, handing the 49ers a first down.

Dawson finished the drive with a 30-yard field goal.

Smith and Kansas City took over with 2:12 left and another chance to rally. But Smith overthrew tight end Anthony Fasano on the second play, and Cox swooped in for an easy interception.

Jamaal Charles ran for 80 yards to pass Larry Johnson (6,015 yards) for second place on Kansas City’s career rushing list. He needs 52 yards to surpass Priest Holmes (6,070 yards) for the franchise record.

On a sun-touched day that sent temperatures into the low 90s in Silicon Valley, both offenses started out hot.

Smith completed six of eight passes for 61 yards on the game’s opening drive, capping it with a 2-yard touchdown pass to tight end Travis Kelce. He directed the Chiefs with precision and poise — converting five consecutive third downs — but struggled to find the end zone again before the break.

San Francisco scored on all three of its possessions in the first half, though the first two ended on Dawson’s big right leg. Kaepernick finished off the third drive where he wanted all along, rolling to his right and lofting a 9-yard TD pass to a wide-open Stevie Johnson to give the 49ers a 13-10 lead.

The Chiefs stopped San Francisco to start the third quarter. Former Oregon standout De’Anthony Thomas ran his first punt return 28 yards, then caught a short screen and sprinted 17 yards for a score to put the Chiefs back in front, 17-13.

But San Francisco stayed focused and never lost its cool. The often-penalized 49ers finished with just two penalties for 10 yards.