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NEW YORK -- Derek Lowe was being given a tour of the Yankees' facilities and changing at a locker without a nameplate Monday afternoon. David Phelps had little more than a day to prepare for a spot start in place of ace CC Sabathia.

No matter. The unlikely duo combined to shut down the potent Texas Rangers.

Phelps pitched a career-high five innings and picked off two runners, and Lowe completed New York's 8-2 victory on Monday night with four shutout innings in his Yankees debut.

"To have those two guys step up to do what they did today, to give those guys like D-Rob (David Robertson) and (Rafael) Soriano a full day off and not have to warm up and anything that's big," said Nick Swisher, who hit a grand slam off Ryan Dempster and drove in five runs.

In the opener of a four-game series between the teams with the AL's best records, the Yankees powered their way to a sixth straight victory over Texas in the Bronx.

Swisher's second slam this season was his 200th career homer. Eric Chavez also homered off Dempster (1-1), the Rangers' recent acquisition. Ichiro Suzuki tripled and Derek Jeter followed with a long RBI double in the seventh to end Dempster's third start for Texas.

Dempster matched a season high by allowing eight runs. The other time he allowed eight was in his first start for Texas on Aug. 2. In three starts since coming from the Chicago Cubs in a trade-deadline deal, Dempster has allowed 19 runs -- 16 earned -- in 17 1/3 innings.

"Too much is made of that," Dempster said of switching leagues. "I know how to make pitches. When you're facing lineups and you don't get that break at the bottom of the lineup where you have the pitcher hitting, and you always have a hitter, every pitch is really, really valuable and it just comes down to executing one pitch at a time. Simple plan. Nothing more and nothing less than that. And tonight, I paid for my mistakes."

Swisher added an RBI single in the seventh as New York won for the fifth time in six games.

Phelps (3-3) was being held to a 75-80 pitch limit. Phelps needed 26 pitches in the first without being hit hard. But thanks in part to a nifty pickoff move, he fulfilled his manager's wish to make it through five innings.

"I really wanted to get him through the fifth inning. I thought it was important for him," Joe Girardi said. "It's important for us, too."

Phelps turned over a 5-2 lead to Lowe in the sixth. Designated for assignment by Cleveland on Aug. 2 and released Friday, Lowe signed with New York earlier Monday and made his first appearance since July 31.

Lowe earned his first regular-season save since 2001 while with Boston, shutting down Texas on two hits. He walked none and struck out four.

Lowe went 8-10 with a 5.52 ERA for the Indians this season, and he had an 8.80 ERA in his final 12 starts for Cleveland.

"I had to get back to hiding the ball a little better," Lowe said. "I'm not going to do jumping jacks because you pitch one good game because you're in this for the long haul."

The 39-year-old right-hander, a longtime rival of the Yankees while he pitched for the Red Sox, received little notice from the fans when his name was called to start the sixth. After retiring three straight in the seventh, the crowd gave him a loud ovation.

The high-powered Rangers had ample opportunities to break open the game early against Phelps, making his fourth start and first since July 4. They scored a run in the first on a broken-bat single by Nelson Cruz and added another when David Murphy led off the second with a homer.

Phelps hit Ian Kinsler with a pitch with two outs in the second. He then picked him off first base to end the inning with Elvis Andrus at bat. Andrus opened the third with a single and advanced to second on Adrian Beltre's infield single with one out. But Phelps picked off Andrus at second for out No. 2.

"They're huge," Phelps said of the pickoffs. "They're two outs where I don't have to throw a pitch."

Phelps is the first Yankees right-hander with two pickoffs in a game since Scott Kamieniecki did it in his big league debut in 1991 at Toronto, according to STATS LLC.

Phelps allowed two runs and six hits. He struck out three and walked one.

Making his first start in the Bronx since 2000, Dempster retired his first six hitters then it fell apart in the third, when seven of the first eight batters reached.

Russell Martin led off with an opposite-field single to right and Raul Ibanez followed with a hit that fell just in front of Cruz, the right fielder. Suzuki, batting ninth for the first time in his career, sacrificed. Jeter fell behind 1-2 before walking to load the bases.

Swisher lined a shot into the second deck in right for the sixth slam of his career and a 4-2 lead. Swisher had not homered since July 19 -- a drought of 61 at-bats -- a day before he injured his hip flexor and missed six games.

New York loaded bases again without making an out, then Curtis Granderson hit a sacrifice fly.

Game notes

The Yankees have hit a major league-leading nine grand slams. ... A moment of silence was held for Red Sox player, manager and broadcaster Johnny Pesky, who died Monday at 92. ... Yankees closer Mariano Rivera (torn knee ligament) played catch on flat ground. Girardi still insisted that Rivera is more than likely not returning this season. "I don't see it happening," he said. ... New York 3B Alex Rodriguez (broken left hand) had a football catch. ... Rangers manager Ron Washington said Andrus will probably get a day at DH this series. Michael Young was working out at shortstop pregame.