Play resumed 14 days, 14 hours and 18 minutes later at 1:05 p.m. when Taylor (1-1) lobbed a ball to Nick Dini, who pinch hit for Viloria and lined out to first base.
Whit Merrifield homered leading off the third for Kansas City.
Tyler Webb (1-1) earned his first major-league victory with one-third inning of work in his 79th career game. He struck out pitch-hitter Ben Gamel.
Baltimore had lost 13 of its previous 14 games, including the series opener to Kansas City on Monday.
The team returned to its practice facility in Kansas City this week to prepare for its third preseason game Saturday night against San Francisco. It had been training in nearby St. Joseph.