Wells, 27, went 2-for-3 with his 10th home run. Montero, 22, also was 2-for-4 and finished his first full season hitting .260 with 15 home runs and 62 RBIs.
Beavan, 23, closed out a strong second half by giving up just seven hits with one walk and no strikeouts. He finished 11-11 with a 4.43 ERA, including an 8-5 record and 3.40 ERA in 14 starts after being recalled from Triple-A Tacoma in midseason.
"It feels great," said Beavan. "I'm going out the way I wanted to go out. Ever since I've been back, I tried to work as hard as I can and harder than I did the first time. It's easy to get a little relaxed when you have success up here. You don't get your mental side of it focused enough and that's the biggest thing I learned is the mindset."
The Mariners jumped on AL Cy Young contender Jered Weaver for two runs in the first with an RBI double by Kyle Seager and a bases-loaded fielder's choice grounder by Montero.
The Angels then removed Weaver, having thrown just 25 pitches, and replaced him with Jerome Williams. Weaver's record dropped to 20-5 and his ERA went from 2.73 to 2.81 in the one inning.
"My body was just kind of shutting down," said Weaver. "I just kind of felt it in the bullpen, the shoulder wasn't really feeling up to par. It's tough to turn it on for games like this."
The Angels, knocked out of postseason contention on Monday, finished 89-73 after losing their final two to Seattle.
"These last two games, when Oakland knocked us out, it was tough to stay concentrated," Angels rookie sensation Mike Trout said. "It's tough to get motivated. It's a long year, you work so hard, and all of a sudden you're out of it, it's tough."
The Mariners have been fighting playoff contenders for most of the past month, however, and weren't about to let down in their final shot.
"We were giving it everything we had til the end," said Wells. "That's characteristic of our ballclub all year. We came up just short in a lot of one-run games that could really sway things our direction if we turn that around next year. All you can do is ride the momentum and positivity. There was a lot of learning for me this year, just getting comfortable with this organization. I'm already excited for Spring Training next year."
The Mariners ended up with their biggest margin of victory over the Angels since a 14-0 win in 1987. They pushed across two more in the third on a two-run double by Montero, then added a two-RBI single by Wells in the sixth.
Wells then capped a six-run seventh with his three-run blast over the hand-operated scoreboard in left after rookie shortstop Carlos Triunfel had laced a two-run single of his own.
Beavan was aided by some strong defense from Wells in right field. Wells made a nice catch on a line drive by Kendrys Morales with two outs in the fourth, getting a late break in the afternoon sun before reaching out to snag the ball before going into a barrel roll near the warning track.
Wells then threw out Trout trying to score on a sacrifice fly in the sixth, the second time he threw out the 21-year-old phenom this series.
"He shouldn't have gone there," Wells said with a smile. "I was way too shallow. I know he's going to be running around. I just got him. I threw out the right lure for the Trout man."
Wells, who finished with a team-high eight outfield assists in just 93 games, impressed Wedge with his play in the past few weeks as the club continued searching for answers in right field after trading Ichiro.
"He raised his hands up there at home plate, he's a little shorter to the baseball and is able to battle a little more," said Wedge. "He's really just scratching the surface with that. That's why we wanted to take a look at him. And he has our attention. You look at the way he plays in the outfield, I think he's as good as anybody. He has the most accurate arm out there and he's athletic. It was impressive the way he finished."
Wells became the eighth Mariners player to hit 10 home runs, the highest total since they had nine in 1997. Only the Yankees had more double-digit home run guys in the AL this season with 10.
Montero threw out Trout trying to steal in the first, leaving the Angels' MVP candidate one stolen base short of being just the third player with 30 home runs and 50 stolen bases in MLB history.
Seager, 24, went 2-for-5 with a double and two runs scored, raising his final average to .259. He wound up leading the team in RBIs (86) and home runs (20) in his first full season in the Majors.
All those youngsters -- along with Dustin Ackley, Michael Saunders, Justin Smoak and a strong core of young pitchers -- are part of the Mariners' nucleus that now heads into an interesting offseason in which the club hopes to add to its offense before reconvening in Peoria, Ariz., next February.