Kovar's goal gave Stanford (3-5-2 in the Pac-12, 9-6-3 overall) some hope of gaining entrance into the NCAA tournament. The team will find out if it did enough when the NCAA selection committee reveals its choices on Monday morning.
"We knew we had to win," Kovar said. "We knew that losing wasn't an option and I think the guys really had that attitude. I'm just proud of the guys and the way they rallied in overtime. We just pulled it out one way or another and still did it."
California was ranked No. 1 for several weeks, with its recent struggles costing it the conference title. The Bears also lost to UCLA and Washington this month.
The Huskies hold their own destiny, with a win Sunday at Oregon State. The Bruins, who play Saturday night at San Diego State, need a win and a Washington loss.
"We set a very simple goal at the beginning of the year, that we wanted to play as many games of soccer as we could," Stanford coach Jeremy Gunn said. "It's a great group of players, three tremendous seniors, and we'll be looking forward to hopefully being selected."
In the latest RPI rankings released Monday, Stanford ranked No. 41, though the win over the Bears should improve that rating. UCLA, Washington, Notre Dame and California, in that order, are the top four teams in the ratings.
"We don't make the selection but you have to look at it and expect us to be in it," Gunn said. "From there we'll be excited to play anybody. We've played nine out of 18 games against top seven or eight opponents, so there can't be too much out there that we haven't seen. I'm thrilled for our players."
The Cardinal has played nine games against teams ranked among the top seven in the RPI ratings, with a 2-6-1 record in those games.
For the second straight match the Cardinal needed overtime to seal the victory. This time it was Kovar picking up a loose ball and weaving his way into the box from 30 yards out, through four defenders before firing with his right foot past Cal goalkeeeper Alex Mangels.
"Earlier in the game I tried passing on one of those, but I just saw it and I'm like 'just keep going.' I ended up getting it on my right foot and firing it past the keeper," Kovar said.
The goal was a fitting end to a match the Cardinal had controlled throughout. Stanford played one of its best halves of the season the opening 45 minutes and only crucial saves from Mangels and a ball cleared off the line by a defender kept the Cardinal from running away with it early on.
"We knew we had a great opportunity against an unbelievable team, and our players were incredible," Gunn said. "The first half couldn't have gone any better for us, other than if we'd gotten another goal. We played some great attacking soccer."
Freshman Jordan Morris was a nuisance for the California defense early on, first getting clear in the seventh minute but firing right into the chest of Mangels. He got another chance in the 14th minute, but again Mangels would be equal to the task.
Despite the stops Stanford was full of momentum and the deadlock was finally broken in the 19th minute on a picturesque counterattack started by Kovar.
The sophomore midfielder gained possession deep in his own end and played a curling deep ball down the left flank to Morris, who beat his defender to the pass.
Morris broke into the box to Mangels' right, bringing the keeper out then tapping into the center for Zach Batteer, who coolly finished with the left-footer for his team-leading eighth goal of the campaign.
Stanford nearly scored again in the 22nd minute as Morris fired low to the far post only to have Mangels tip the shot wide. The ensuing corner kick was cleared of the box but Ty Conklin served it back in towards the far post, where Mangels came off his line in an attempt to punch out but came to a stop outside the six-yard box.
Brandon Vincent, who scored the winner in Sunday's match at Oregon State, went high and headed towards the open goal but a California defender reacted in time to clear the attempt before it could reach the line. Kovar's ensuing corner kick was headed just wide by Batteer.
For the half Stanford outshot California, 11-1, and forced Mangels and the defense into four saves. The plot took a twist as the second half got underway, leading to California's equalizer in the 52nd minute.
Ryan Neil served a corner kick into the box but Mason Case's header was blocked. A scramble for the loose ball ensued and in the fracas the Cardinal was whistled for handling the ball in the box, awarding a penalty kick to the Golden Bears.
Alec Sundly stepped up to the spot and sent Drew Hutchins the wrong way to knot the match up at 1-1.
Hutchins, however, bounced back to give the Cardinal life late in the match, making a pair of excellent saves. First the Cardinal keeper denied a close-range effort from Nick Lima in the 79th minute and just four minutes later again rejected Lima, keeping things even on the scoreboard.
Stanford had a great opportunity in the 89th minute when Batteer hustled around a defender to rescue a ball off the Cal goalline and break into the box. He fed Eric Verso for the left-footed shot but the Cardinal forward's initial hesitation allowed the Golden Bear defense to converge and Verso's shot was blocked.
"Regardless of results this season, you have to look at how the team has responded and played," Gunn said. "We've been absolutely magnificent. The attitude from the players, the work rate, the soccer, it's been so consistent no matter how good the opponent's been."
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