During parts of two seasons with the Yankees, reliever Andrew Miller kept with tradition and stayed perpetually clean-shaven. When he returned to the Bronx on Friday as a member of the Cleveland Indians, Miller sported a noticeable swath of facial hair, looking more relaxed.  Miller, who said he preferred not to shave, is no longer distracted by the trade rumors and role changes that shadowed him during his time with the Yankees this season.  “I’m ready to just get back to baseball,” Miller said. “I think it’s kind of been one distraction after another the last few months. I’m happy to be on a team that, obviously, baseball is the focus the rest of the way. I’m looking forward to that.”  Miller’s homecoming illuminated a stark contrast between the immediate futures of the Indians and the Yankees.  The Yankees are in transition, punctuated further by Mark Teixeira’s announcement Friday that he will retire at the end of the season. The Indians are aspiring to reach the playoffs for only the second time in nine seasons and were determined buyers at the nonwaiver trading deadline as they chase their first World Series title since 1948.  In the third inning Friday, Starlin Castro hit his first career grand slam, and Teixeira added two hits with two runs scored as the Yankees stymied the Indians’ quest for one night with a 13-7 win.  “For him, what he went through earlier and the emotions, it had to be really rewarding for the game that he had tonight,” Yankees Manager Joe Girardi said of Teixeira.  Indians starter Josh Tomlin was jostled around before leaving in the fifth, having given up seven runs on nine hits. The Indians used three relievers, but Miller did not make an appearance.  Using Miller even when trailing by several runs would not have been outlandish. On Thursday, Miller entered a game against the Twins in the sixth inning.  “The way he feels about the game is so refreshing,” Indians Manager Terry Francona said. “O.K., we got one of the elite relievers in the game, but we also got a guy that’s willing to pitch at the most opportune times of the game. That makes him even better than his numbers.”  Before Miller was traded last Sunday for four minor leaguers, he had shuffled from closer to setup man and back. Through the commotion, Joe Girardi described Miller on Friday as “a guy that impacted our clubhouse and our team in a year and a half as much as anyone I’ve ever seen.”  Sam Manchester will guide you through the 2016 summer Olympics in Rio de Janeiro.  Hey. It’s Sam from the NYT Sports desk. I’m going to the Olympics in Rio (so you don’t have to :) ). Grab a limited spot and I’ll text you updates, answer your questions and share the behind-the-scenes stuff nobody else gets.  Thanks! Talk to you soon.  Standard messaging rates may apply. Your information is used only to deliver messages about the Rio 2016 Olympics.  Watching from afar, Francona said Miller’s willingness to adapt was “very attractive to us.”  Combining Miller with the right-handers Bryan Shaw and Cody Allen, the Indians now have their own impressive bullpen triumvirate. Whereas the Yankees used Betances strictly in the seventh inning, Miller only in the eighth and Chapman in the ninth, Francona is less inclined to maintain such a hierarchy.  “We’ll kind of pitch them whenever it makes sense and all three are on board with that,” Francona said, later adding: “It helps a lot. Having good bullpen pitchers is important. Sometimes you get your hands tied a little bit by having somebody supposedly throwing the one eighth inning or ninth inning. I’ve never been a huge fan of that, and to be able to have some flexibility is really important.”  Entering the game, the Indians’ bullpen had a 3.66 E.R.A., fifth best in the A.L.  Even after Jonathan Lucroy vetoed a trade from the Milwaukee Brewers to the Indians, Francona said his team appreciated the aggressive pursuit of Miller by the Indians’ president of baseball operations, Chris Antonetti, and the front office, making clear the franchise’s intention to win now.  “It doesn’t guarantee anything, but it certainly gives us a better bullpen,” Francona said.  The postseason is a more distant dream for the Yankees, but they were placated Friday by a dose of nostalgia with Teixeira’s multiple-hit game and some encouraging signs for the future. The rookie Rob Refsnyder picked up two hits, and another rookie, Gary Sanchez, drove in two runs and threw out two runners in his first career start at catcher.  “He has the ability to throw a lot of runners out,” Girardi said of Sanchez.  Girardi said Friday that Teixeira had told him his goal for the rest of the reason was to help the Yankees reach the playoffs. It was a stoic company line from a player who has repeatedly been hailed as a model teammate.  As for the Indians, the Miller acquisition clearly demarcated their proximate plans.  Describing his team’s mind-set, Francona quoted Theo Epstein, his former colleague with the Boston Red Sox and the current president of baseball operations for the Chicago Cubs, who traded for Chapman days before Miller was dealt: “If not now, when?”  “We have a chance, and when you have a chance, like I said, there’s no guarantees, but man, coming to the ballpark sure is fun,” Francona said.  A version of this article appears in print on August 6, 2016, on page D7 of the New York edition with the headline: Castro’s Slam Helps Yanks Top Indians. Order Reprints| Today's Paper|Subscribe
Mark Teixeira had two hits and scored twice on Friday night. Andrew Miller did not play in his return to New York after being traded last Sunday.