Carlos Santana also homered for the AL Central leaders, who improved to 23-12 at home by pulling out a game that was delayed by rain in the eighth inning for 1 hour, 57 minutes.
"I guess it was worth the wait," manager Manny Acta said of the Indians' eighth win in their last at-bat at Progressive Field.
Shin-Soo Choo singled off Tim Wood (0-1) with one out in the 11th for his third hit and stole second. Wood intentionally walked Santana to face Phelps, who came up hitting .100 (2 for 20) since being called up from Triple-A Columbus on June 8.
"It was a fastball in," Wood said. "He did exactly what he's supposed to do with a belt-high fastball. My sinker's my best pitch. I had faced him a few times (in the minors) and got him out."
Tony Sipp (3-0) worked a scoreless 11th to help the Indians win for the fifth time in seven games and move to 6-0 in interleague play. Their sweep extended the Pirates' losing streak to 13 games in AL ballparks. Pittsburgh has not won a road interleague game since June 17, 2009, at Minnesota.
Sipp and five other relievers worked six scoreless innings. Cleveland's bullpen has not allowed a run in 22 2-3 innings over seven games.
The offense has been another story. Before the game, the Indians announced that hitting coach Jon Nunnally had been replaced by Bruce Fields, the organization's minor league hitting instructor. Acta said the decision was made before Cleveland's 5-1 win on Saturday night.
"It was very tough, one of my toughest days of work," Acta said. "Yesterday we won the game and didn't feel like celebrating. I understand that some (players) are a little upset, but we have to do what's best for our team."
Phelps' liner into the right-field seats made Cleveland 1 for 7 with runners in scoring position Sunday
-- and 18 for 116 (.155) since June 2.
Pittsburgh manager Clint Hurdle lamented the Pirates' offensive struggles, too. They totaled three runs in the series following a four-game winning streak. Prior to that, they scored four runs in going 1-3
"We left 14 men on base," Hurdle said. "At the end of the day, that's a lot."
Acta was much more upbeat following Cleveland's seventh sweep of a series of at least three games this year.
"How about that bullpen?" he said. "They kept us in the game. Oh, and by the way, a pretty good series."
Acta and other Indians could not stop talking about a defensive gem by Asdrubal Cabrera. The shortstop made a barehand stop of a sharply hit one-hopper on the outfield grass and threw out Brandon Wood in the top of the 10th.
"Half the dugout was saying it was the best play ever," Acta said.
Added Phelps: "That was nasty. I became a fan right there and said,
'Ohhhh!'"
Neil Walker and Matt Diaz drove in first-inning runs off Justin Masterson to put Pittsburgh ahead 2-0.
Walker followed a one-out triple by Xavier Paul with an RBI single. Walker took third on a single by Garrett Jones and scored as Diaz grounded into a forceout at second.
