The Yankees threatened to break it open in the seventh and eighth innings, but Lackey and Oliver each met the challenge before Fuentes sealed the deal with a perfect ninth.
"You know you aren't going to get a whole lot of runs with CC going," Lackey said. "You've got to hold down their offense. It's fun. I enjoy those kinds of challenges. If you want to be at the front end of a rotation, you've got to enjoy them -- and make a few runs count."
Having scored a total of 24 runs in the first two games, the Angels busted loose with a four-run fourth inning against Sabathia. Bobby Abreu once again was a pivotal factor against his former teammates.
After Maicer Izturis singled leading off, Abreu lashed an RBI double to left. Following a one-out walk by Gary Matthews Jr., Howard Kendrick went the other way for an RBI double to right. After Brandon Wood's infield out brought home Kendrick from third, Robb Quinlan stroked an RBI single to center.
"You know Bobby enjoyed this series," Chone Figgins said, Abreu having driven in six runs in the three games while going 6-for-13. "He makes every at-bat count. He just never gives in, and I think that's had a positive impact on all of us."
Figgins, who singled and tripled in four at-bats to take a .310 average, .393 on-base percentage and 68 runs scored into the All-Star break, showcased his glove in support of Lackey.
With the bases loaded and none out in the seventh, Lackey struck out former teammate Mark Teixeira with a 3-2 breaking ball and got Alex Rodriguez to bang into an inning-ending double play started by Figgins at third.
"That's not just another team," Lackey said of the Yankees, who are 5-17 in their past 22 games in Anaheim and 17-32 overall in their past 49 against manager Mike Scioscia's troupe. "I definitely think as a club we play better to the better competition. You can't really explain it. It's just the way it happened."
After the Yankees had scored twice and loaded the bases with one out in the eighth, Oliver got pinch-hitter Nick Swisher to lace a line drive right back to the mound. The veteran lefty gloved it and went to first to complete a rally-killing double play.
"It got there in a hurry," Oliver said, grinning. "A ball hit that hard, it's just reaction. It happened so quick."
His teammates marvel at the unflappable nature of Oliver, the club's elder statesman at 38. He continues to age like a fine cabernet, going to the break 3-0 with a 3.00 ERA in 32 appearances, with 28 strikeouts against 11 walks in 39 innings.
"That's pretty impressive," Lackey said. "I'm just hoping to be walking around at his age. Seriously, D.O.'s probably been our most consistent guy out there [in the bullpen]. He's a good guy to have out there holding a lead for you."
So is Fuentes, who is on his way to St. Louis as the Angels' lone All-Star representative. The lefty put away three of the game's toughest outs -- Derek Jeter, Teixeira and Rodriguez -- without a ripple, striking out A-Rod to notch his MLB-high 26th save in 29 chances, shaving his ERA to 3.23 in 34 appearances.
"He had a couple of rough ones early in the year," Scioscia said, "but he has been lights out since then. The one thing that's kept us confident in the bullpen is Brian's consistency."
Lackey worked out of jams in the third and sixth innings before Melky Cabrera led off the seventh with a double to left-center field, scoring on Jorge Posada's pinch-hit single to center.
When Brett Gardner grounded to first, Kendry Morales -- a defensive replacement for Wood -- threw the ball into left field for an error, putting two runners aboard.
Jeter's two-strike single to right field loaded them for Teixeira, who worked the count full before striking out on a breaking ball -- Lackey's 107th pitch.
"Tex, obviously being a great hitter, you can't throw it in the dirt," Lackey said. "It has to be a great curveball that's also a strike. Tex has a great eye."
On a 1-1 count, A-Rod grounded sharply to third, where Figgins made the play on a difficult hop, stepped on the bag and doubled up Rodriguez at first on a dig by Morales.
"I read it right, I guess," Figgins said. "Morales has been doing a great job of picking balls."
Figgins' two-out triple to the left-center-field gap and Izturis' full-count single added an insurance run in the seventh, ending Sabathia's day.
Lackey (4-4) departed having yielded two runs on six hits in seven innings, walking three and striking out six. Sabathia slipped to 8-6.
A draining first half now brings a much appreciated break for the Angels, who find themselves in first place in the AL West, having made it there with an impressive kick.