Moore (8-0) gave up one run, struck out three and walked one. The left-hander has won nine straight decisions, breaking the franchise record of eight set last year by David Price.
The Rays' ninth win in 11 games put them a season-high three games over .500 (23-20) and lifted Tampa Bay into a third-place tie with skidding Baltimore in the AL East. The Rays had been in fourth since April 20.
Adam Jones had two hits, stole two bases and drove in a run for the Orioles, who have dropped five straight - all at home.
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