The Royals only piled on from there, ultimately tagging Tillman for six runs in 5 2/3 innings en route to a 7-3 win on Saturday night at Camden Yards.
"It's more a mental battle when that happens," Tillman said of the delay. "You've got to go in the game, and it just didn't work out for me."
With the rain coming in spurts, players struggled to figure out when the game would actually start.
Only adding to the delay was a pregame ceremony for Hall of Fame first baseman Eddie Murray, who became the fourth of six O's legends to have his statue unveiled.
"It was a challenging night," manager Buck Showalter said. "They did a better job with it than we did."
The loss knocked the Orioles from their perch atop the American League Wild Card standings. The O's are now tied with the Tigers, trailing Oakland and Tampa Bay by a half game.
Tillman had allowed only two home runs in six starts this season before being tagged for three in three innings on Saturday, all off of his cutter.
"Frustrating night, I was working up in the zone," Tillman said. "Didn't have my breaking ball going. Didn't have it the whole game."
Alex Gordon hit Tillman's third pitch of the night over the left-field wall, marking the 14th first-inning run the right-hander has given up in seven starts this season.
Salvador Perez extended the Royals lead to 3-0 in the second, turning a belt-high cutter into a two-run homer that landed in the first row in left.
Billy Butler completed the trifecta in the third, hitting another belt-high offering out to right-center to put the Royals up by four, all while Tillman battled hamstring cramps.
"Not ideal conditions," Tillman said. "They played the same game, same field, same rain delay. I had to battle through that."
After a pair of quiet innings, Tillman ran into more trouble with two outs in the sixth. Tillman hit Perez and surrendered a walk to Jeff Francoeur, before being pulled for Miguel Socolovich, who gave up an RBI single to Eric Hosmer on his first pitch.
During the next at-bat, Hosmer broke for second, drawing an errant throw from catcher Matt Wieters that allowed Francoeur to steal home and make it 6-0.
Gordon notched the second two-homer game of his career with a solo shot in the seventh, extending the Royals lead to 7-0 to make a difficult day for the O's even worse.
"It is tough," O's outfielder Nate McLouth said. "All players have their routine, and I would guess it would be hardest for the pitchers because they have their warmup routine, their whole game day routine."
That was hardly the case for Royals starter Luis Mendoza, who held the O's scoreless through his first six innings.
Still, Royals manager Ned Yost was far from secure.
"Those guys have the propensity of battling back in those games," Yost said of the O's. "It was the seventh inning and we were up 7-0, but I didn't feel safe."
The O's did everything they could to justify those fears with a surge in bottom of the seventh.
After Wilson Betemit walked and Chris Davis singled to lead off the seventh, Manny Machado continued to pay early dividends, doubling in the O's first run with a sharp grounder down the third-base line.
Omar Quintanilla drew the O's within four at 7-3, with a two-run single, and McLouth moved him to third with a double to right.
But Adam Jones' grounder up the middle was snared by Alcides Escobar, whose throw to first beat Jones by a step, ending the O's best chance at yet another dramatic comeback.
"We have to keep it closer early on," Showalter said. "We had a couple of chances to get back in it, but hit some balls at them."
The O's hit back-to-back singles with two outs in the first, but Wieters popped out to left.
With men on the corners and two outs in the fourth, Chris Davis struck out to end the threat.
Those chances were some of the best the O's would get, as they went down in order in the eighth and ninth.
In all, the Orioles left seven men on base, including three on third.
"It was a couple two-out situations, and those are tough to deliver," McLouth said. "Sometimes you do and sometimes you don't. But [Mendoza] pitched well, and we'll go out and get them [Sunday]."