Teibert, a 20-year-old from Niagara Falls, Ont., is in his third season, but had not managed to score while playing sparingly most of the time.
The Whitecaps (3-4-3) ended a seven-game winless streak and beat the Galaxy for the first time.
The Galaxy (4-3-2) were unbeaten in five previous regular-season meetings and also eliminated the Whitecaps in the opening round of the playoffs en route to a second consecutive MLS championship.
Darren Mattocks also scored for the Whitecaps, while Gyasi Zardes replied for L.A.
All of the scoring came in the second half.
Teibert's second goal on 76 minutes proved to be the winner as it gave Vancouver a 2-0 lead. He sent a through ball to the corner of the L.A. box where Gershon Koffie promptly passed it back to him for a left-footed strike.
After Teibert scored, teammate Jun Marques Davidson jokingly neatened the Canadian's mohawk to make sure all hairs were pointing upward.
Scoring chances were few and far between in the first half, but both clubs still had a couple of dangerous opportunities. In the fifth minute, Vancouver goalkeeper Joe Cannon dove to stop a Jose Villarreal header.
Eight minutes later, L.A. goalkeeper Carlo Cudicini caught a Darren Mattocks shot from about 25 yards out.
Teibert entered the game after Vancouver midfielder Daigo Kobayashi left in the 14th minute with an injury. Kobayashi was unable to continue due to a knock suffered about three minutes earlier.
Teibert quickly made an impact as he provided a nice cross from the right flank for Mattocks, who sent a header to the far post only to watch Cudicini corral the ball.
In the 23rd minute, L.A.'s Omar Gonzalez shot wide on a rush through the middle as the ball went off a Vancouver defender. Five minutes later, the Galaxy's Sean Franklin fired a shot way over the net.
Cudicini came up big again on 37 minutes as he stopped an inadvertent volley by teammate Gonzalez off Vancouver midfielder Nigel Reo-Coker's blocked shot.
Teibert opened the scoring for the Whitecaps in the 63rd minute as he took a pass from Reo-Coker near the right corner of the L.A. box, cut back towards the middle and fired in a left-footed shot.
After netting his first MLS goal, Teibert pumped his fist in the air and ran to the Whitecaps bench and hugged teammates.
After Teibert's second goal increased Vancouver's lead, Zardes cut the Galaxy's deficit in half in the 86th minute as he headed in a Villarreal cross from the right flank.
But Mattocks secured the win in stoppage time as second-half substitute Jordan Harvey chested the ball to him near the goal-line and he jammed it past Cudicini.
Notes: Vancouver lost Camilo late in the second half. His departure resulted in Harvey subbing on to set up the insurance goal. Honduran international central defender Johnny Leveron started his first home game for the Whitecaps. He received a yellow card for a tackle on which he twisted Jose Villarreal's legs in the third minute. ... Contrary to expectations, L.A. striker Robbie Keane and Todd Dunivant, who are recuperating from injuries, did not dress.