After going 2up early on, Kuchar never trailed in their quarter-final encounter at Dove Mountain and sealed victory with a two-putt par at the short 16th.
"I'm going to keep plugging away, wear guys out," Kuchar said greenside after recording five birdies and three bogeys.
A four-times winner on the PGA Tour who has reached the last eight in this tournament three years in a row, Kuchar will next face either Australian Jason Day or Northern Ireland's Graeme McDowell.
Day was 1up on McDowell after 11 holes on a sun-splashed afternoon in Arizona's high desert.
In the other two quarter-final matches, defending champion Hunter Mahan was 1up on U.S. Open winner Webb Simpson after 10 holes while Ian Poulter, the 2010 Match Play champion, was 4up on American Steve Stricker after 13.
Kuchar birdied four of the first nine holes to take early control against Garrigus, rolling in a 28-footer at the par-four ninth to go 3up.
Garrigus made a complete mess of the 10th after his drive ended up in an unplayable lie in the desert to go four down.
But Kuchar then lost momentum, bogeying the 11th and 12th and losing the par-five 13th to a birdie for his lead to be halved.
However, Kuchar rebounded with a four-foot birdie putt at the driveable 15th to go 3up before wrapping up the win on the next hole.
Earlier in the day, the third round was played to get the tournament back on track after only three-and-a-half hours of golf was possible on Wednesday because of driving sleet and then snow at Dove Mountain.
The players set off in a two-tee start to the third round before the winners headed out again in the quarter-finals after a quick turnaround.