Mitch Moreland had three hits and drove in a run for the Rangers, who also got three hits from Elvis Andrus in their fourth consecutive victory, snapping the Angels' three-game winning streak.
Chris Iannetta doubled in the go-ahead run and Luis Jimenez got his first career RBIs on a two-run single while the Angels took a 6-3 lead in the sixth inning, but Texas tied it with three runs in the seventh.
Pierzynski then hit his fourth homer of the season to right off Angels closer Ernesto Frieri (0-1).
Tanner Scheppers (2-0) pitched two innings of one-hit relief for the Rangers, and Joe Nathan worked the ninth for his sixth save.
Josh Hamilton had four hits against his former team after getting bumped out of the cleanup spot, and Howie Kendrick had a two-run double for the Angels in the series opener between AL West rivals coming off weekend sweeps. Los Angeles beat defending AL champion Detroit three times by a combined 22-4, while the Rangers won three straight over Seattle during their only home series in a 19-day span.
Albert Pujols went 0 for 5 for the Angels, while Mike Trout was 0 for 4 with a walk, missing a potential run-saving catch at the wall in the sixth inning before flying out in the ninth.
But Hamilton went 4 for 4 after getting dropped to the No. 5 spot in the lineup for the first time in his debut season with the Angels, who gave him $125 million to leave Texas last winter. Mired in a 1-for-21 slump, Hamilton moved down and immediately had his 16th career four-hit game—his first with the Angels.
Derek Holland yielded six hits and six runs for Texas, walking four while pitching into the sixth inning in his rockiest start of a strong season.
Joe Blanton yielded 12 hits while pitching into the seventh for the Angels, leaving with a three-run lead before his bullpen wasted it. The veteran right-hander had a standout spring training after signing with Los Angeles as a free agent, but has struggled mightily this month while starting 0-3.
Los Angeles went ahead with a three-run fourth inning, but Texas tied it in the sixth on back-to-back doubles by David Murphy and Moreland, whose drive to left appeared to be eminently catchable for Trout, the normally stellar fielder who got moved from center field to left this season.
Iannetta delivered a two-out RBI double to left in the sixth, chasing Holland. Jimenez followed with his two-run single off Jason Frasor for the rookie third baseman's first career RBIs.
But the Rangers' first six hitters all reached base in the seventh during a small-ball rally against four Angels pitchers. Pierzynski drove in a run, and another scored on a groundout before pinch-hitter Jeff Baker tied it when Scott Downs dropped his high chopper in front of the plate.
NOTES: Hamilton hit in the No. 5 spot just three times last season for Texas, but went 4 for 10. Opponents have walked Pujols five times this season to get to Hamilton, including twice on Sunday.