Bernardez jumped on a loose clearance off a last-ditch cross from Shaun Francis. Real Salt Lake goalkeeper Nick Rimando went up against Earthquakes forward Alan Gordon to try and punch it clear, but the ball barely made it out of the visitors' 6-yard box, allowing Bernardez to hammer it home. The final whistle sounded just after the ensuing kickoff.
The draw extended San Jose's unbeaten streak at Buck Shaw Stadium to 21 games in all competitions. The Earthquakes used another 95th-minute goal, this one from Gordon, to force a 1-1 tie with top-seeded Mexican side Toluca in the first leg of the teams' CONCACAF Champions League quarterfinal Tuesday.
Chris Wondolowski also tallied for the Earthquakes, who had lost their regular-season opener to RSL in three of the previous four seasons.
Joao Plata scored his second goal in as many games for RSL, which was bidding for a second straight win to start the season under new coach Jeff Cassar. Kyle Beckerman and MLS rookie Luke Mulholland also scored first-half goals against San Jose goalkeeper Jon Busch.
Wondolowski scored in the sixth minute from point-blank range, using his right thigh to redirect Bernardez's flick header of a long free kick by Shea Salinas.
Beckerman equalized for Real Salt Lake just five minutes later. Plata laid off a ball into space for Beckerman to strike with his left foot from 27 yards. The shot ricocheted in off the right post.
Plata initiated and finished RSL's second goal-scoring sequence in the 32nd minute, beating two defenders from the left wing, trading give-and-go passes with Luis Gil and deking Earthquakes center back Jason Hernandez before pulling a 12-yard strike just inside the near post.
Mulholland put RSL up 3-1 in first-half injury time, racing past a scrambled San Jose defense to pick up the rebound of Ned Grabavoy's shot and slot it home from 8 yards.
Bernardez gave San Jose life in the 75th minute, connecting with a Salinas corner on a near-post run and skimming his header to the open back post.