Rodriguez took a no-hitter into the seventh before walking and retiring another batter before Keinner Pina singled to right field to give Burlington their first hit. After the hit, Rodriguez was replaced by reliever John Hayes.
Rodriguez finished with a line of two earned runs on one hit over 6 and 1/3 innings. Rodriguez also struck out four and walked five.
The Whitecaps were leading 5-0 in the top of the seventh before Burlington went on to score four runs in the inning. Another Burlington run in the eighth tied the game at 5-5.
The game remained tied until the top of the 10th inning when Burlington scored three runs. The Whitecaps scored a run of their own in the home half but eventually fell 8-6.
Colby Bortles and Reynaldo Rivera each had two RBIs for the Whitecaps while Rivera, Jordan Pearce and Ignacio Valdez all had two hits.
West Michigan is now 18-15 on the year and in fourth place of the Midwest League Eastern Division, three games behind first place Bowling Green.
The Whitecaps will continue their home series against Burlington on Friday at 7:05 p.m.