They also made sure the Texas Rangers must wait a little bit longer for their big finish.
Conger and Hideki Matsui scored after early extra-base hits for the Angels, who have won the past three division titles and aren't willing to give it up just yet. Los Angeles pulled within one game of .500 with its ninth win in 12 games, putting a solid finish on a disappointing season.
"It was very impressive," said Santana, who has beaten the Rangers three times this season. "Me and Conger were on the same page the whole game. It's not easy, because they're a great team. It takes a lot of focus."
With ample help from Conger behind the plate, Santana (17-9) dominated the Rangers' potent lineup during his fifth career shutout, striking out eight and holding Texas without an extra-base hit in its fourth loss in five games.
Conger was recalled from the minors two weeks ago, but the Angels' heralded prospect has caught two shutouts in his first four major league starts. His catcher's ERA is 1.50 after being behind the plate for Jered Weaver's shutout last week in Cleveland.
"That's all on the pitchers," said Conger, who alertly took third base on his first career extra-base hit. "They've been throwing great. Everything was working for him. He executed in a couple of tight spots. It's the first time I've caught all of these pitchers, so I'm just trying to get them to pitch to their strengths."
Santana got more support than Colby Lewis (11-13), who yielded just four hits and struck out 10 in seven strong innings. The Texas right-hander had won his past two starts after a nine-game winless streak, but his teammates never reached third base against Santana.
"No, I'm not frustrated," Lewis said. "What are we, seven, eight games (ahead) still? We've just got to get this thing clinched. I think it's coming down (to the wire), and we're maybe putting a little bit too much stress on ourselves to try to clinch and get it done instead of just playing the way we've been playing the last week-and-a-half leading up to the last couple of games."
The Rangers still are in good shape to clinch their first AL West title since 1999, even if it takes a few days more than they hoped. Texas' lead over second-place Oakland, which beat Chicago 7-2, slipped to seven games, and its magic number stayed at six.
"(Lewis) pitched extremely well, once again," Rangers manager Ron Washington said. "We've just got to put a couple of runs across the plate when we get a chance, and everything else will take care of itself. We just needed runs tonight. We certainly got the pitching out of Colby. He was extremely good tonight."
Santana had won 16 games twice previously in a career spent entirely with the Angels, but the Dominican right-hander is having perhaps his best season.
Santana faced the minimum 13 batters through 4 1-3 innings, giving up a leadoff single to Vladimir Guerrero in the second inning but erasing him with a double play. He stranded a runner in scoring position in the sixth, seventh and eighth innings, striking out Elvis Andrus and Michael Young to end the eighth in dramatic fashion.
"He's pitching against a team that has power throughout the lineup, and he ended up shutting them down," Angels manager Mike Scioscia said. "He's got great velocity this year, and he's matching it with command. You put that package together, and you're seeing a guy that's stepping forward and having a breakout year."
Santana's last shutout was also against Texas on Sept. 28, 2009. He moved into eighth place on the Angels' career strikeouts list with 849, passing Rudy May.
Conger led off the second inning with a triple off the wall and scored easily on Kevin Frandsen's groundout. Los Angeles cobbled together another run in the fourth when Matsui hit a leadoff double, advanced on a fly ball and scored while Mitch Moreland made a throwing error.
NOTES: Lewis struck out 10 batters for the fifth time this season. ... 1B Kendry Morales returned to Angel Stadium and made his first extensive public comments since breaking his leg May 29 while jumping on home plate to celebrate a game-ending grand slam. Morales is still bewildered by his injury, but said he's slightly ahead of schedule in his rehabilitation and expects to be back at full strength for 2011. The Cuban slugger is eligible for arbitration in the offseason. ... Texas RHP Frank Francisco resumed his throwing program and could be back on the mound by next week, but still might not be recovered from a strained muscle in his right side in time for the playoffs.