Johnson (2-1) went six innings, matching his longest outing, and allowed four runs on 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.
Brandon Lyon pitched the ninth for his 10th save in 12 chances for Arizona, which avoided its first three-game losing streak. 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.
The Diamondbacks gave Johnson plenty of support. They took a 1-0 lead in the first on Conor Jackson's RBI single.
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 Eric Bruntlett.
The Diamondbacks exploded for five runs in the fourth, when Eaton couldn't find the strike zone.
He walked Justin Upton and Miguel Montero around a double by Mark Reynolds to load the bases with no outs.
After retiring Augie Ojeda on a fly to shallow center, Eaton walked the .167-hitting Johnson on four pitches to tie it at 2.
Chris Young's fielder's choice grounder gave the Diamondbacks a 3-2 lead, and then Drew hit a 1-2 delivery 385 feet to right field for a three-run homer.
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.
Notes: 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. ... 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. ... Arizona RHP Micah Owings (4-1) faces the Phillies on Wednesday night. In his last two starts, Owings has allowed 11 earned runs in 10 2-3 innings.
