San Jose finished the game with 10 men, but held on for all three points despite a late push from the Timbers.
Bernardez netted from the spot in the 55th to open the scoring after Andrew Jean-Baptiste's foul on Shea Salinas won the home team a penalty.
Lenhart doubled the lead three minutes later.
Salinas was once again responsible for the creation of the goal, curling in a free kick from the left that Lenhart was able to slide in and get a foot on, putting it past goalkeeper Donovan Ricketts who was trying to come off his line to make the save.
Darlington Nagbe pulled one back for Portland in the 83rd, and two quick-fire yellow cards to San Jose's Marvin Chavez made for a very nervous finish for the home fans, who suddenly found their team up just one goal and down a man.
Frédéric Piquionne had a chance to tie things up in the 88th with a header and Nagbe and will Johnson each had chances in stoppage time as well, only to see their team come up short in a bid for a late equalizer.