NEW YORK -- Jordan Montgomery watched Wilson Ramos drive his first-pitch changeup to deep center field and his heart sank, thinking he gave up a grand slam in a pivotal game.

A few seconds later, Montgomery exhaled and tapped his chest to express his appreciation toward Aaron Hicks for going over the fence and catching the ball.

Hicks made that critical catch on Ramos in the top of the first inning, and Montgomery pitched six effective innings as the New York Yankees clinched at least home-field advantage in next week's wild-card game with a 6-1 victory over the Tampa Bay Rays on Tuesday.

"It kind of just happened," said Hicks, who also robbed Los Angeles Angels infielder Luis Valbuena of a grand slam on June 14.

The Rays loaded the bases with no outs on two singles and a walk in the first inning, and Montgomery survived his first scare when Logan Morrison hooked a fastball foul into the right field seats. The left-hander struck out Morrison before Ramos swung at the first pitch.

Ramos drove the ball straight for the vicinity of the 385-foot sign in front of New York's bullpen. Hicks began racing toward the wall off the bat, leaped and stuck his glove over the fence. He made the catch with the ball barely staying in his glove before throwing it in. The play became a sacrifice fly instead of a grand slam.

"I was worried off the bat, but Aaron can cover a lot of ground," Yankees manager Joe Girardi said. "He's very athletic, and it saved the day."

Montgomery (9-7) turned around on the mound and watched the entire sequence unfold. He then fanned Adeiny Hechavarria to end the inning, and he and the other fielders congratulated Hicks as they headed into the dugout.

"I've seen a couple (similar plays), but the way his arm got over, it was impressive," said Montgomery, who couldn't recall a more impressive catch in any game he pitched before Tuesday. "Body control, he was hitting the wall, caught it, brought it in. It's like he jumped and then he glided into the wall, caught it and hit the wall."

After Hicks' catch, Montgomery settled in. He wound up allowing one run on six hits, earning him another start in the Sunday regular-season finale against the Toronto Blue Jays. Hicks' catch and Montgomery's ability to pitch well helped the Yankees move within three games of the American League East-leading Boston Red Sox after they fell five games out two days ago.

Once Montgomery completed his 28th start, he went over to Hicks and said: "Thanks for saving me."

Ramos was philosophical about the play.

"As soon as I hit the ball, I hit the ball well, but not enough," said Ramos, who nearly hit his fourth career grand slam. "But I connected on that ball really well, especially in this stadium, small stadium, the balls carry. That was a homer. He jumped and he stole that. He stole that homer, but it's part of the game. You've got to keep your head up and keep going."

The catch was part of an eventful return for Hicks from a second disabled-list stint caused by an oblique injury. As scheduled, he played six innings in his first game since Sept. 2. Hicks went 0-for-1 with an RBI, walked three times and stole a base as his belt fell off.

Hicks' second walk was part of New York's four-run second inning that knocked out Blake Snell (4-7).

Starlin Castro opened the inning with his 15th homer before Hicks and Aaron Judge drew bases-loaded walks. The Yankees scored their fourth run when Ronald Torreyes scored on a wild pitch by Chaz Roe before adding two in the eighth on RBI singles by Gary Sanchez and Matt Holliday.

The Rays lost for the 11th time in 17 games, and this defeat meant their official elimination from postseason contention after they were within a half-game of the second wild-card spot in early August.

"We fell apart a little bit offensively," Tampa Bay manager Kevin Cash said. "We just couldn't get anything going. We had some opportunities and couldn't capitalize. ... It was kind of a slow death, which is not fun and frustrating to a lot of the guys in the clubhouse."

Also frustrating for the Rays was Snell's shortest career start. He lasted one-plus inning, allowing four runs on four hits.

NOTES: New York RHP Adam Warren (back spasms) threw two innings during a simulated game without difficulty. When he does return, manager Joe Girardi said Warren likely would appear in two games before the postseason. ... Tampa Bay INF Matt Duffy (heel) played three innings and took three at-bats in an instructional league game Monday. ... Former heavyweight champion Mike Tyson watched batting practice on the field and posed for pictures with New York 3B Todd Frazier. ... Tampa Bay 3B Evan Longoria went 0-for-3 and is hitless in his past 10 at-bats. ... A fan was ejected in the eighth inning for yelling out where Tampa Bay C Wilson Ramos was positioning his glove during an at-bat by C Gary Sanchez.