Travis Hafner's second-inning, solo homer put the Indians ahead, and Mike Redmond's RBI double in the fifth gave them a two-run lead that vanished after Peralta's rushed throw with two outs.
Rookies Scott Sizemore and Austin Jackson had hits and scored runs in the pivotal inning.
Rick Porcello (1-0) gave up two runs in five-plus innings, Phil Coke and Joel Zumaya combined for three innings of scoreless relief and Jose Valverde got his first save in two chances.
David Huff (0-1) allowed four runs - just one earned - in six innings.
The game drew 45,010, the most for a Comerica Park opener and the second-largest crowd in the ballpark's 11-year history. Some of the loudest ovations were for the sun, which peeked through the clouds occasionally on an afternoon with temperatures hovering around 40 degrees.
Ordonez gave the fans reasons to clap and cheer at other times. The outfielder, who entered batting .500, hit a two-run double in the seventh that scored Jackson and put Detroit ahead 5-2.
Miguel Cabrera was 0 for 3 with a walk after starting the season on a tear at the plate, helping the Tigers win two of three at Kansas City.
Sizemore and Jackson made a solid first impression, playing at Comerica Park for the first time, while Johnny Damon went 0 for 4. He is 0 for 13 over the last three games.
Hafner's 396-foot drive to right-center leading off the second and Redmond's RBI in the fifth seemed to give Cleveland a chance to keep having success early this season on the road while Huff started with four scoreless innings.