In his second spring start, Santiago allowed only one hit and struck out five. He hasn't permitted an earned run in 6 2-3 innings this spring.
"That was the highlight," Angels manager Mike Scioscia said. "That's four strong innings."
Santiago was 4-9 with a 3.56 ERA for the White Sox last year.
Cubs prospect Jorge Soler hit a go-ahead triple in the ninth. Luis Valbuena doubled and scored in the seventh.
Chicago starter James McDonald worked two scoreless innings.
Angels slugging prospect C.J. Cron, who hit a tying, three-run homer in the ninth on Thursday, delivered an RBI single in the eighth.
"C.J.'s looking very comfortable," Scioscia said. "The growth he's shown the last year and a half has been noticeable."
Angels: Santiago said he tried a new approach after he was unimpressed with his pregame bullpen warmup session.
"Today we worked away, away then got them off the plate and then attacked," he said.
Valbuena was the only Cubs projected starter in the lineup, but it made no difference to Santiago.
"I don't think about who's up there," said Santiago, who said he threw six or seven screwballs. "I just blacken them out and attack the zone."
Santiago is competing with Joe Blanton for one of two open sports in the bullpen. On Friday in a split-squad game against Colorado, Blanton gave up seven earned runs and four homers in 3 1-3 innings. He's coming off a 2-14 season with a 6.04 ERA in 2013.
Cubs: McDonald was significantly better than his debut, when he allowed six runs in one inning of relief against the Angels, including a grand slam to Mike Trout.
A former prospect with the Dodgers, he went 2-2 with a 5.76 in six starts with Pittsburgh in 2013. He spent time with four different Pirates minor league affiliates last year while struggling with a strained right shoulder.
The Angels got good news on right-hander Dane De La Rosa, who left Thursday's game with tightness in his right forearm. X- rays showed that De La Rosa, 6-1 with a 2.86 ERA in 75 games with the Angels in 2013, had no damage and just a strain.
Scioscia said he would "play it by ear" on how De La Rosa would be used throughout spring. He is expected to be ready by opening day and De La Rosa told reporters that it "wouldn't be long" before he'll be back in regular action.
De La Rosa walked five and allowed a grand slam to Scott Van Slyke against the Dodgers.
Former Chicago Bears linebacker Brian Urlacher took batting practice with the Angels and shagged fly balls prior to Friday's game. He said he was impressed with Trout, who he called "a little brick" and said he had no doubt he could play football.