He didn't know how good.
"I didn't know it was gone, to be honest," Drew said. "I knew I hit well. I knew I hit it on a line. I didn't know if I had enough height to get it out."
Drew's homer capped a five-run outburst against Eaton (0-1) in the fourth inning and made a winner of Randy Johnson (2-1), who earned his 286th victory.
With the victory, the Diamondbacks improved to a majors-best 22-11 and avoided their first three-game losing streak.
By stopping a skid, Johnson reprised a familiar role from his glory days in the desert.
He said his surgically repaired back felt better than it has all season, and it showed early on, when he retired the first five Phillies.
But then Johnson's control lapsed, and he yielded four runs over the final four innings.
"I felt great at the beginning of the game," said Johnson, who tied Robin Roberts for 27th on the all-time victory list. "It's probably the best I've felt all year as far as my back, my presence out there. Then I just lost my control a little bit and got a little frustrated with the execution of some of my pitches."
Johnson went six innings, matching his longest outing, and allowed four runs, six hits and struck out six. He also surrendered two homers, walked two and hit a batter.
The Big Unit gave up a total of five earned runs in his first three starts after returning from back surgery. In his last two outings, Johnson has allowed 10.
The Arizona bullpen shut the Phils out over the final three innings to preserve Johnson's victory.
Brandon Lyon pitched the ninth for his 10th save in 12 chances, but not without a bit of drama. Lyon gave up singles to Carlos Ruiz and Shane Victorino before retiring Eric Bruntlett on a foul fly to right field to end the game.
Johnson said the bullpen "tends to get not as much credit as it should. But I think with our bullpen, it's incredible."
The Diamondbacks' hitters also gave Johnson plenty of support, starting with Conor Jackson's RBI single in the first.
The Phillies rallied in the third on a double by Eaton, who was hitless in his first 10 at-bats this year, and a two-run homer by Bruntlett.
The Diamondbacks exploded for five runs in the fourth, when Eaton couldn't find the strike zone.
After retiring Augie Ojeda on a fly to shallow center, Eaton walked the .167-hitting Johnson on four pitches to tie it at 2.
"It's pretty pathetic," Eaton said.
It was also Johnson's first RBI since Oct. 2, 2004.
"Bases loaded, a big guy up there, I don't want to pitch to him," Arizona manager Bob Melvin said with a chuckle.
Chris Young's fielder's choice grounder gave the Diamondbacks a 3-2 lead, and then Drew homered to make it 6-2.
"Fourth inning was the story of the game," Phillies manager Charlie Manuel said. "[Eaton] had three walks, walked the leadoff guy in the inning, he walks the pitcher with the bases loaded with four pitches. That was a big moment in the game."
The Phillies cut it to 6-3 on Bruntlett's RBI double in the fifth and pulled within two runs on Jayson Werth's 418-foot homer to center field in the sixth.
Although the Phillies left seven men on base and committed two errors, Eaton took the blame for the loss. "You don't mind losing if you're beat, and when you beat yourself, that's when you really mind," he said. "I don't think Arizona beat us today. I beat ourselves."
Philadelphia LF Pat Burrell went 0-for-3 and struck out twice against Johnson. He's 4-for-22 (.182) lifetime with 14 strikeouts against the Big Unit. ... The Diamondbacks have had an extra-base hit in all 33 games and lead the majors with 120. ... Johnson is 10-3 against Philadelphia. ... Arizona 3B Chad Tracy, who is returning from a knee injury, was to begin a rehabilitation stint at Triple-A Tucson on Tuesday night. The Diamondbacks want him to have about 40 at-bats before he rejoins them. ... Bruntlett has hit safely in 13 of his last 14 games (16-for-53, .302). He has two doubles, a triple and a homer in that span.