NEW YORK –- CC Sabathia did not fully appreciate his first visit to Cooperstown, N.Y., representing the Indians in the annual Hall of Fame Game nearly two decades ago. A Minor Leaguer then, he had no spare time to set foot in the museum, settling for a glance from the bus as it rolled toward the highway.

As the 14th pitcher in history to record at least 250 victories and 3,000 strikeouts, Sabathia has all but guaranteed a second opportunity to tour those hallowed grounds. The left-hander succeeded in his fourth attempt at the milestone on Wednesday, hurling six strong innings to help the Yankees complete a series sweep of the Rays with a 12-1 victory at Yankee Stadium.

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“It’s crazy to put my name up there with some of those guys that I idolized, some of those names that are enshrined in baseball history," Sabathia said. "To be a part of that, it’s a big deal. It’s fun to have those numbers.”

Gary Sanchez hit a three-run homer as part of a six-run first inning and Gleyber Torres later added his first career grand slam as the Yankees won their fifth consecutive game, swelling their advantage in the American League East to a season-high 3 1/2 games.

The Yankees have homered in 22 consecutive games, three shy of a franchise record and the longest streak in the Majors this season. Tampa Bay's Blake Snell, the reigning American League Cy Young Award winner, threw 39 pitches and generated just one out before being sent to the showers.

"We have a really good offense," DJ LeMahieu said. "It really doesn't matter who's out there; we have a chance to score a lot of runs. Snell didn't look like he had his best stuff. We had really good at-bats and it was good to get on him early."

Sabathia had been winless in three starts since returning from the injured list June 2, and said he fiddled with the grip on his cutter between starts. Sanchez said the pitch made a difference on Wednesday as Sabathia limited Tampa Bay to a run on three hits, striking out seven with three walks.

That cutter is what Sabathia credits for his late-career success, having borrowed the pitch from former teammate Andy Pettitte -- coincidentally, the most recent pitcher to reach 250 wins, who did it with the Yankees in 2013.

"I’ve been able to play with some great players like Andy Pettitte and Mariano Rivera," Sabathia said. "Just thinking about the second half of my career, learning the cutter and where that’s taken me -- if I hadn’t learned that pitch in 2014, I’d probably be out of the game."

No longer the fireballer of his youth, Sabathia has had to rely on deception and guile, pushing his body toward the finish line despite a degenerative right knee condition and -– more recently –- an offseason heart procedure that delayed his season debut for a couple of weeks.

"He's a great leader here in the clubhouse," shortstop Didi Gregorius said. "Guys love him. That's who you want to be around all the time. It's unbelievable with everything he went through, and he's still out there fighting for the team. That shows how big his heart is for the game."

Each of the previous 13 pitchers to reach 250 wins and 3,000 strikeouts are enshrined in the National Baseball Hall of Fame, with the exception of Roger Clemens.

“I think he’s a lock," Yankees manager Aaron Boone said of Sabathia. "This is it for him. I think in five years, they come calling.”

"His career is a Hall of Fame career," Sanchez added. "The 250 wins represent that, the 3,000 strikeouts that he has. A great career overall."

Speaking in the Yankee Stadium press conference room with his wife, Amber, and their four children seated in the front row, the former Indians' and Brewers' ace reflected upon what many view as an inevitable date with history.

"Just to have somebody mention your career as being a Hall of Fame career means a lot," Sabathia said. "I’ve been blessed to have played with some great teams, been around some great organizations and great players. A lot of it just rubbed off.”

Sabathia said it is particularly meaningful to be listed alongside fellow African-American hurlers Bob Gibson and Fergie Jenkins in the select group.

“That means a lot, being an African-American pitcher, being from the inner city and wanting this game to grow back again in the inner city," Sabathia said. "Having the chance to put up these numbers and have some of these kids know that I’m from where they’re from. I love this game of baseball. Hopefully it opens doors to some kids to open their eyes to start playing.”

LeMahieu laced a two-run single that capped scoring in the big first inning –- LeMahieu's second hit of the frame -- and Torres’ slam came as the Yankees put six more runs on the board in the seventh. The Yanks have won seven of nine meetings with the second-place Rays this season, and 22 of 29 games against American League East opponents.

“I think that’s the biggest thing, coming out today and getting that sweep," Sabathia said. "Getting that win, making a statement that we’re a pretty good team. We're going to keep going.”