After Ervin Santana made it through five innings in his season debut, showing he had recovered from a sprained right elbow with 92 pitches, the Angels needed five relievers to finally nail it down. They combined to yield one earned run across seven innings, striking out nine.
"A great win for the team, in every respect," said Jason Bulger, who pitched out of serious trouble in the top of the 12th to pick up his first win of the season and second of his career.
With the bases loaded and one out, Bulger struck out Dustin Pedroia with a 95-mph heater at the knees and retired David Ortiz on a slow roller that Mathis scooped up and fired to first.
Losing for the fourth time in six meetings with the Angels, the Red Sox got five hits from Julio Lugo and 15 overall but left eight runners stranded in the final five innings and 17 for the game.
"We were dodging bullets all afternoon," Angels manager Mike Scioscia said. "They were 3-for-21 with runners in scoring position. That's a lot of pressure to put on yourself."
The Red Sox could have won it in 10th if not for another Herculean play in center field by the great Torii Hunter, who stole a home run from the Royals' Miguel Olivo to save Sunday's win.
Off with the crack of the bat from right-center, Hunter made a backhanded catch running full-tilt as he approached the warning track. Calling to mind Willie Mays' memorable catch-and-throw on Vic Wertz in the 1954 World Series, Hunter whirled and fired it back into the infield, keeping Jacoby Ellsbury stationed at second base.
"That was a great play," Pedroia said. "That's why he's got a truckload of Gold Gloves [eight]. He saved the game for them and kept them going. That's why he's the best."
Hunter drove in the first three Angels runs against Brad Penny. After Bobby Abreu's two-out single in the first, Hunter sent one against the wall in left-center, beyond Ellsbury's grasp, for a triple to give Santana a lead.
In the third, Hunter raked a two-run double down the left-field line to cash in Mathis and Chone Figgins after they singled. Figgins was flying around the bases.
Santana, for his first time out against a dangerous lineup, fared well enough to satisfy the boss. The 2008 American League All-Star had his fastball consistently in the 91 to 93-mph range and buried his slider in good spots when he needed to, notably on Ortiz to leave the bases loaded in the fourth inning.
"This is what we wanted from Ervin -- about 90 pitches  in a Major League environment," Scioscia said after his club's ninth win in its past 11 games. "He pitched well. As his mechanics come together, he'll be more efficient with his pitches."
It was 3-3 in the bottom of the seventh when Penny's final pitch was slashed into the right-field corner by Aybar, who turned on the jets -- only Figgins among the Angels is as fast -- for a triple. Mathis' sacrifice fly cashed him in with the go-ahead run.
Mathis has been phenomenal this season with runners in scoring position, hitting .471 in 17 at-bats after his game-winning hit against Delcarmen.
"It's not like I'm going up with a different approach with runners in scoring position," Mathis said. "You bear down a little more. I got some pitches I could handle and was lucky some balls fell in."
The Red Sox tied it against Scot Shields in the eighth with a run on consecutive two-out singles by Lugo, Ellsbury and Pedroia.
Abreu, after banging a triple off the center-field wall, was thrown out at home to end the eighth by right fielder J.D. Drew on Hunter's fly ball.
In trouble throughout, runners on base in each inning with the leadoff man getting on four times, Santana set the tone by making big pitches when he needed them, finishing with five strikeouts against three walks.
Mike Lowell's leadoff double in the second led to a tying run on Lugo's two-out hit, and Pedroia doubled leading off the third and scored on Jason Bay's groundout. A leadoff walk by Drew produced a run in the fourth on Ellsbury's two-out single, but Santana left the bases loaded in striking out Ortiz, who went 0-for-7.
"We got a game plan going into it [against Ortiz] and our guys executed it well," Mathis said. "He's a great hitter, and to hold him down is an accomplishment.
"On that last at-bat [against Bulger], he checked his swing and didn't get out of the box great, so I knew I had time to get around it and make the play. Jason threw a great breaking ball there after he'd been throwing some mid-90s heat to him."
Darren Oliver was dominant in the sixth and seventh, striking out five hitters while allowing a double to Pedroia. After Shields, Brian Fuentes worked a scoreless ninth, stranding two runners, and Jose Arredondo got through the 10th (with Hunter's assistance) and 11th before turning it over to Bulger with one out in the 12th and a runner aboard.
"Our bullpen did the job today," Hunter said. "Those guys were dealing."
And Hunter, as usual, was stealing.