After back-to-back singles by Cruz and Jones opened the fourth inning, Wieters hit a ball to second that shortstop Yunel Escobar dropped on a potential double-play attempt while moving the ball to his throwing hand for an error.
They tied the game on J.J. Hardy's sacrifice fly to left, but stranded two runners in scoring position when Steve Clevenger struck out and Steve Pearce grounded to third to end the inning.
Archer left the game after five innings and 100 pitches, allowing three runs on seven hits with six strikeouts and one walk.
“He's a really good pitcher, and he's got really good stuff,” Flaherty said. You've got to grind him, and we were able to do that and get him out of that game.”
The Rays took a quick 2-0 lead on Tillman four batters into the bottom of the first inning as Evan Longoria took an 0-2 pitch over the center field fence for a two-run homer with two outs.
Pearce got the Orioles onto the scoreboard with his first homer of the season to lead off the third inning, a towering solo shot to left on a 3-2 pitch.
Tillman escaped a two-on, two-out jam in the fifth, inducing an inning-ending force play at second from Desmond Jennings.
With the game tied in the eighth, Wieters led off with a single and Clevenger hit a one-out single.
The row of lights went out before Pearce stepped up to the plate. Players from both teams went back to their dugouts before the game resumed.
“Have you been in the minor leagues? I've seen it a couple times — two, three times — and it lasted a lot longer than that,” Showalter said about the delay. “There's a bank behind home plate that never comes on. Everybody's waiting for those to come on, and they don't ever come on. I was just hoping it wouldn't mess up the air conditioning.”
Pearce then drew a walk to load the bases, setting the stage for Flaherty's hit, which came off Rays reliever Joel Peralta.
Closer Tommy Hunter stranded the bases loaded in the ninth inning for his ninth save in 10 opportunities as the Orioles bullpen tossed three scoreless innings in relief of Tillman.
Darren O'Day (1-0) picked up the win taking over for Tillman and pitching the seventh.