"Maybe the bullpen kind of appreciated me going out and pitching deeper in the game," Eaton said.
Everyone on the Phillies had to love Eaton's effort.
Eaton (7-4) pitched out of a pair of jams, made a nifty defensive play to help his cause and won for the fourth time in five starts.
The Phillies sandwiched this shutout and Jon Lieber's gem around a 17-5 loss to Kansas City on Sunday. They have lost six games this season when allowing a double-digit run total and have come back to win the next game five times.
"That's baseball. You can always come back and start from scratch," manager Charlie Manuel said.
Burrell hit his eighth homer of the season in the second off Javier Vazquez, and Howard's 13th homer in the fourth went deep into the second deck in right.
Rollins made it three solo shots for the Phillies in the sixth when he hit his 11th homer.
"They hit three good pitches," Vazquez said.
That was enough run support for Eaton in his first career start against the White Sox. He was outstanding for the second consecutive outing after his awful, two-inning stint in a 13-0 loss to San Francisco.
Of course, the Phillies won 5-2 the next day.
"Sometimes you're going to get beat and get beat bad. But you've got to come back and win the game," Burrell said.
Vazquez (3-5) allowed only one other hit and struck out four with one intentional walk in six innings. But the punchless White Sox were shut out for the fifth time this season, tied for most in the AL.
"We're wasting a lot of good pitching," White Sox manager Ozzie Guillen said. "It seems like a movie. You want to change the tape, but it's the only one you have. I don't have answers."
It was Philadelphia's second shutout of the year.
Eaton ran into his first jam in the fifth when he allowed back-to-back singles to open the inning. But he struck out Josh Fields, made a headfirst dive to snare Vazquez's bunt and retired Rob Mackowiak on a grounder before walking off the field to a rousing ovation.
The pitcher escaped again in the sixth. With one out and the potential tying runs on base after consecutive walks, Jermaine Dye struck out swinging before Eaton worked his way back from a 3-0 count and got Juan Uribe to fly out.
Eaton pumped his fist at catcher Rod Barajas as they walked off the field.
The Phillies badly needed Eaton to give them a lift after the momentum from a three-game sweep at the NL East-leading New York Mets was wiped out when they lost two of three to the lowly Royals.
"I was trying to be aggressive in the strike zone and force those guys to put the ball into play early," Eaton said.
Jim Thome, the former Phillies slugger and fan favorite who led the NL with 47 homers in 2003 before he was traded to the White Sox in 2005, didn't play. He was on deck when the game ended, ready to enter as a pinch hitter.
"We didn't want Thome getting up there where he could tie or win the game for them," Manuel said.
Without the designated hitter in use during this interleague series, Thome wasn't expected to get a start in his first trip back to Philadelphia until Wednesday.
- Phillies RHP Freddy Garcia, on the disabled list with a shoulder injury, had an MRI exam that showed fraying in the rotator cuff and a problem in the labrum. Garcia will seek a second opinion.
- The Phillies will promote RHP Kyle Kendrick from Double-A Reading to start against the White Sox on Wednesday. He'll replace Garcia. Kendrick was 4-7 with a 3.21 ERA at Reading.
- Chicago 3B Joe Crede was examined by specialists so they could get a look at his inflamed lower back. He could be headed for surgery.
- Burrell's 196th homer moved him into seventh on the team's career list.