Miller (2-2) struck out six, walked a pair and scattered five hits over five frames, throwing 91 pitches to pick up the "W" five days after he held New Orleans to a run over five innings for his first Triple-A victory.
The right-hander worked into and out of trouble in the first inning when Anthony Rizzo singled to load the bases following consecutive walks to leadoff man Brett Jackson and Dave Sappelt. Miller struck out Luis Valbuena and Welington Castillo and then popped up Adrian Cardenas to escape the jam.
Miller worked a 1-2-3 second, struck out Jackson and Sappelt in the third, and, with runners on the corners in the fourth, he caught Travis Wood looking to end the frame.
Valbuena doubled with two outs in the fifth, bringing the tying run to the plate, but Rizzo popped up to third baseman Zack Cox to end the inning and Miller's afternoon.
Miller, the Cardinals' Minor League Pitcher of the Year for the past two seasons, entered his first Triple-A season as the No. 5 overall prospect in baseball and the No. 2 right-handed pitcher behind Atlanta's Julio Teheran. He's 2-2 with a 4.50 ERA with 25 strikeouts and eight walks in 18 innings.
St. Louis' first-round pick in 2009 allowed four runs in each of his first two starts, taking losses against Oklahoma City. He split the 2011 season between Class A Advanced Palm Beach and Double-A Springfield, finishing 9-3 with a 2.70 ERA in 16 starts.
Adron Chambers, Ryan Jackson and Bryan Anderson drove in the runs for Memphis on Tuesday, while Travis Wood (1-2) allowed two runs -- one earned -- and struck out eight over six innings to suffer the loss for the Cubs. Wood was acquired with Sappelt during the offseason from the Reds in the deal that sent Sean Marshall to Cincinnati.