Walker (1-2) struck out five and allowed only an unearned run.
The Rangers, on the same day they reacquired 2010 AL MVP and five-time All-Star slugger Josh Hamilton in a trade with the Los Angeles Angels, missed a chance to win consecutive games for the first time this season. Texas is the only AL team without consecutive victories.
After rain delayed the start of the game for 55 minutes, Yovani Gallardo (2-3) walked the first two batters.
There was a fielder's choice grounder before Cruz put Seattle ahead to stay with his single through the right side of the infield. That was the majors-best 21st RBI for Cruz, who played in Texas from 2006-13.