Miller (1-2) routinely fired fastballs clocked into the mid-90s past hitters before turning the game over to the bullpen in the seventh.
Only Aramis Ramirez managed to break through off Miller hitting a solo homer in the fourth. The Brewers have just one run and six hits over the first two games of the three-game set with their NL Central rival.
Marco Estrada (1-1) took the loss after allowing three runs over six innings.
The right-hander, who was off to a good start with a 2.31 ERA entering Tuesday, had a little uncharacteristic trouble with his command. He hit Yadier Molina with a pitch in the second and threw a wild pitch in the fourth.
Still, Estrada allowed just five hits, which would have been more than adequate pitching during the Brewers' long winning streak.
But that was before Milwaukee had to face the aces from St. Louis.
On Monday night, Lance Lynn shut down the Brewers, striking out 11 over seven innings. Miller was just as effective. He got Jean Segura to ground out to second and caught Ryan Braun looking on a 94 mph fastball to start the fourth.
The only big mistake was a fastball down the middle of the plate that Ramirez turned on for his second homer and team-best 12th RBI.
Miller, a 23-year-old righty, recovered nicely to end the fourth by getting Jonathan Lucroy to hit a one-hopper to first.
The Cardinals had built a 3-0 lead by the top of the fourth to back Miller. After missing the season's first 13 games with left knee tendinitis, Ellis made a nice debut by driving in a run in the second on a groundout, and another in the fourth off a sacrifice fly.
St. Louis could have picked up a few more runs if not for a few blunders around the bases.
Allen Craig had an RBI double in the third but the inning ended after Estrada spun around to successfully pick him off. An inning later, both Matt Adams and Peralta were thrown out in rundowns in between third and home.
NOTES: Kolten Wong had started 12 of the team's first 13 games at second until Ellis rejoined the club. Manager Mike Matheny said he didn't necessarily have a plan on how he would split playing time. "We just watch how he's going, watch how Kolten's going," Matheny said. "Realize that we have a very, very good option there at second base and just kind of take it day by day." ... The Cardinals were 8-1 on Tax Day since 2005 entering Tuesday's game. ... Brewers manager Ron Roenicke managed his 500th career game to become the sixth skipper in franchise history to reach that plateau with the organization. ... The teams wrap up the three-game set with a Wednesday matinee. The Cardinals' Joe Kelly (1-0) will be opposed by the Brewers' Wily Peralta (1-0) on the mound.
Link to box score: St. Louis (9-5) 6 at Milwaukee 1
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