Mike Napoli's third-inning RBI single was all the offense the Red Sox needed to come out on the positive end of a pitcher's duel for the first time this season. Boston was 0-18 when scoring fewer than three runs.
Workman (1-0) walked one and struck out four in earning his first win as a starter since last July. He held the Orioles hitless until Ryan Flaherty lined a soft single to center with two outs in the sixth.
Workman had to overcome two stoppages, both in the second inning. The first lasted 15 minutes, the second 1:18.
"It wasn't that bad," Workman said. "I went down and threw in the batting cage a little bit to stay loose, to stay ready."
After retiring Nick Markakis to end the sixth inning, Workman got two straight outs in the seventh before being lifted. It was the longest outing of a 27-game career that includes seven starts.
"He was outstanding, especially in light of the two different rain delays," Boston manager John Farrell said. "He was able to stay loose with a couple of almost simulated innings in the batting cage."
Workman retired the first 13 batters before Nelson Cruz drew a walk. J.J. Hardy followed with a popup to second base, and Cruz took off for second and was easily doubled up.
"It's no excuse," Cruz said. "I should know better. It shouldn't have happened."
Earlier, Boston third baseman Xander Bogaerts robbed the Orioles of two potential hits in the third inning. He snagged a bunt by David Lough and threw out the fleet runner, then made a diving stab of a line drive by Flaherty.
The no-hit bid gained steam later, but Workman said, "I was not really thinking about it. I was just trying to stay in the moment and keep executing pitches and keep working each batter. Not getting ahead of myself."
Workman will have a hearing Friday on his appeal of a six-game suspension. He was suspended after the league determined he was intentionally throwing in the "head area" of Tampa Bay's Evan Longoria on May 30.
If he is forced to miss time, Workman certainly went out on a high note.
"Honestly, when we started back up, I thought if he got through four innings that might be enough for tonight," Farrell said. "But as efficient as he was, as strong as he was, he just kept putting up zeroes and retiring guys consecutively so we continued to stay with him."
Tillman (5-3) gave up one run and seven hits in six innings. It was his first loss in six starts since May 11.
"Tough conditions tonight for both teams but you won't hear any excuses from us," the right-hander said
Manny Machado started at third base for the Orioles despite receiving a five-game suspension and a fine for intentionally throwing his bat in Sunday's game against Oakland. Machado appealed the suspension, batted second and went 0 for 4, making the final out on a strikeout.
Tillman got off to a rocky start following the second rain delay. Brock Holt led off the third with a single, David Ortiz walked and Napoli delivered a two-out, opposite-field RBI single to right.
Boston used three straight singles to load the bases with no outs in the fourth. Tillman struck out Holt, then got Bogaerts to bounce into a 6-4-3 double play.
Over the first four innings, the Red Sox had seven hits and three walks but scored only the one run after stranding seven and hitting into two double plays.
Red Sox GM Ben Cherington said before the game that an overhaul of the roster is not yet necessary for the struggling team. "I'm betting on the players we have in there," he said. ... Holt extended his hitting streak to a career-high 10 games. ... Wei-Yin Chen makes his 10th career start against the Red Sox in the series finale Wednesday night. He's 3-3 with a 5.26 ERA. Rubby De La Rosa will start for Boston. ... Markakis' 14-game hitting streak ended. ... Baltimore's Chris Davis went 0 for 3 with three strikeouts.
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BALTIMORE, MD - JUNE 10: Manny Machado #13 of the Baltimore Orioles looks on before a baseball game against the...