Boston dropped to 4-15 since holding a nine-game lead over the Rays in the AL wild-card race on Sept. 4. Tampa Bay went into Saturday night's game at Toronto trailing by two games.
The Red Sox and Yankees play a day-night doubleheader Sunday before Boston travels to Baltimore for a season-ending three-game series.
Freddy Garcia (12-8) pitched six innings of six-hit ball, making his case for the No. 3 spot in the Yankees' postseason rotation. Before a regular-season record crowd of 49,556 at the new Yankee Stadium, the AL East champion Yankees used their "A" lineup for the opener of the series that was pushed back by a rainout Friday. They quickly roughed up Jon Lester (15-9).
By the ninth, all the starting position players except Nick Swisher were out of the game.
Montero hit the fourth homer of his brief big league career, doubled in two runs in the third and had an RBI single in four at-bats. Russell Martin backed his declaration of dislike for the rival Red Sox with a two-run single.
Boston had been 6-0 at Yankee Stadium this year and 11-4 against New York overall. Lester had already beaten Garcia twice this season and had won each of his last four starts in the Bronx.
Red Sox manager Terry Francona sought input from his players and coaches after Friday's rainout and shook up his lineup, moving Carl Crawford to the second spot and dropping Adrian Gonzalez to fifth with Dustin Pedroia hitting third.
But it all unraveled in a span of six batters in the second.
With runners on first and second, shortstop Marco Scutaro went deep into the hole to field Andruw Jones' grounder. He seemed to have a chance to get the lead runner at third base but stumbled slightly and had to throw across his body to second. His throw was late, leaving the bases loaded.
Montero then hit a sharp grounder out of Scutaro's reach for the first run. Martin followed with a sinking liner to left field that hit off the glove of a sliding Crawford for two more runs.
Jeter, whose batting average is up to .297 after a first-half slump, followed with a drive into the right-field seats to make it 6-0. Before the game, the Yankees captain carried the bat Roger Maris used to hit his 61st homer onto the field as part of 50th anniversary ceremony.
Lester gave up a two-out, two-run double to Montero in the third and was done, having given up eight runs. After Lester retired the first four batters, the Yankees were 8-for-12 against him.
The short outing — 55 pitches 2 2/3 innings — might make it easier for Francona to use Lester on short rest in Wednesday's regular-season finale.
Boston's starters fell to 3-10 with a 7.34 ERA in the last 19 games.
Garcia allowed 15 runs in his last three outings but kept Boston at bay with slow breaking pitches. On his final batter, Garcia fielded Scutaro's comebacker and nonchalantly pounded the ball in his glove before tossing to first.
Montero, the Yankees' top prospect, connected off Junichi Tazawa in the sixth for his fourth homer in 51 major league at-bats. All his home runs have gone to the opposite field in right.
Notes:
The game lasted 2 hours, 59 minutes — speed baseball as far as these two teams go…Yankees RHP Phil Hughes (back) threw 35-40 pitches in a bullpen session. He said he felt no pain and expects to pitch in Tampa Bay next week. He said he didn't object to pitching out of the bullpen in the postseason if that's what manager Joe Girardi decides. "Just being part of it is special," he said…Francona said he's still unsure how Kevin Youkilis (sports hernia) can help the team. "He's will to try to do anything we ask him to do," said Francona. The Red Sox are going to give it a couple more days to see how he feels…Michael Jordan watched the game from a suite…Boston's John Lackey and Tim Wakefield face A.J. Burnett and Ivan Nova in the split-doubleheader Sunday.