The Angels forced an extra frame when they rallied with four runs over the seventh and eighth innings, but the Orioles clawed back ahead in the top of the 10th.
Reimold got aboard on a fielder's choice against Garrett Richards (1-3) after Adam Jones had led off with a single and went to second on J.J. Hardy's groundout.
That brought up Pearce, who lined a single to right field. Reimold rounded third and seemed likely to be thrown out at home, but Mark Trumbo's throw was up the line and catcher Hank Conger missed with a swipe tag, allowing the decisive run to score.
Reimold also cracked a solo homer and finished with two RBI for the Orioles, who took their second win in three games against Los Angeles.
Pearce finished 3-for-4 while Hardy and Manny Machado each added solo homers.
Trumbo belted a two-run homer for the Angels, who fell for the sixth time in eight games.