Tampa Bay leads the major’s with 90 homers and 286 runs. The Rays have allowed 160 runs.
“So, overall with the offense I am very, very happy,” Rays manager Kevin Cash said.
Zach Eflin (6-1) allowed three runs, four hits and struck out eight for the Rays (34-14), who improved to 21-3 at home this season. It ties the 1978 Boston Red Sox for best start at home through 24 games since 1901.
Despite the great start, the Rays hold just a 3 1/2 game lead over Baltimore (30-16) in the tough AL East.
Jason Adam entered with two on in the ninth and retired both his batters to get his sixth save.
“We're in a good position.” Milwaukee manager Craig Counsell said. “We've had some adversity. That's how a season works. We're going to have to go through this stretch with what we got, and that's not at full strength, That's the way it's going to go.”
Ramírez had a first-inning opposite-field solo homer to right off Eric Lauer (4-5) before Díaz connected on a three-run shot to center in the second that put the Rays up 4-0.
Miller extended his career-best hitting streak (12 games) and on-base stretch (21 games) with a leadoff shot in the third. The homer ended Milwaukee's scoring drought at 23 innings.
Anderson's two-run drive during the fourth cut the deficit to 4-3, and gave the outfielder his third homer and eighth hit in 22 at-bats against Eflin.
Tampa Bay regained a three-run lead, at 6-3, and chased Lauer when Bethancourt went deep to center and Manuel Margot had an RBI single.
“We needed to keep adding,” Cash said. “They pressured us throughout the course of the game.”
Lauer, who was coming off his first relief appearance of the season last Sunday, allowed six runs, six hits and three homers in three-plus innings. The lefty has given up seven long balls over 12 innings in his last three outings.
Milwaukee's Christian Yelich had a RBI infield single in the eighth when his pop up that went 55 feet from the plate dropped near the mound between three Rays players.
ALMOST AN OUT
Brewers SS Willy Adames caught a pop up by Paredes that struck a catwalk in foul grounds, which made it a dead ball. Paredes was retired when Miller, at third base, made his second of his three diving plays on grounders that ended up with an out at first. Sunday is the second anniversary of Adames' trade from Tampa Bay to Milwaukee.
Brewers 1B Luke Voit (neck) was sent to Triple-A Nashville for a rehab assignment. ... RHP J.B. Bukauskas (cervical strain) went on the 15-day injured list and RHP Colin Rea was recalled from Nashville.
Rays: 1B Díaz (groin) started after sitting out four games. He finished 3 for 4, and has a 13-game hitting streak, dating to May 3.