Bauer, who entered with a team leading 2.57 ERA, struggled in the first inning, surrendering four runs to the Sun Devils (37-5, 13-4 Pac-10).
After Drew Maggi singled to start the game, Bauer walked Zack MacPhee and Kole Calhoun to load the bases.
Riccio Torrez quickly made the walks hurt by sending a base hit to left that scored Maggi and MacPhee. Zach Wilson followed with a single that scored Calhoun. Later in the inning, Raoul Torrez capped the big first inning with an RBI single to left.
ASU got another run in the second inning thanks to some heads up base running. Maggi reached on an infield single and stole second.
With two outs, Bauer threw a wild pitch that got away from catcher Trevor Brown and Maggi scampered all the way around and scored to make it 5-0.
UCLA (30-9, 7-7) threatened to get back into the game in the third inning against Kelly. After hitting the leadoff hitter, Kelly got a double play ball, which would loom large later in the inning.
Tyler Rahmatulla reached on an infield single and Blair Dunlap followed with a base hit. Kelly then walked Cody Regis to load the bases.
Cody Keefer then dropped down a perfect bunt for a base hit that scored Rahmatulla to make it 5-1. Kelly didn't let the inning get out of hand, however, by getting Chris Giovinazzo to ground out.
ASU had a similar situation in the fifth, but it had the bases loaded with nobody out and only got one run. After loading the bases, Raoul Torrez struck out for the first out. Matt Newman then hit a sacrifice fly to left that got the only run of the inning, because Austin Barnes grounded out.
Kelly put the first two runners of the sixth inning on, but again got a big double play, this time off the bat of Beau Amaral.
With a runner on third and two outs, ASU head coach Tim Esmay went to freshman Brady Rodgers, who got the final out of the inning.
Rodgers pitched the final 3 1/3 innings, allowing just two hits and striking out four to pick up his third save of the season.
Kelly wasn't sharp control wise, but battled through 5 2/3 innings, allowing just one run on six hits and four walks to pick up his team leading ninth win of the season.
The Sun Devils will go for the sweep in the top five matchup tomorrow afternoon in Los Angeles. Sophomore Jake Borup will get the start for ASU and will be opposed by junior Rob Rasmussen (6-1, 2.85 ERA) at 1PM.