Inter controlled the match from the start and opened the scoring in the 20th minute when Joaquin Correa picked out an unmarked Dzeko whose right-footed shot in the penalty area beat Plzen keeper Jindrich Stanek.
The Czech champions spent most of the game defending and faced an uphill battle after Pavel Bucha was sent off in the 61st minute for a dangerous tackle that caught Inter midfielder Nicolo Barella on the shin.
The visitors doubled their lead 10 minutes later on the counter attack when Dzeko turned provider with a clinical pass that allowed Denzel Dumfries to slot home.
Plzen brought on attacking players after they went down to 10 men but never really threatened and finished the match with only one shot on target to Inter's seven, with the visitors controlling nearly 70 percent of possession.
Inter coach Simone Inzaghi said with three matches in six days, he needed to rotate his squad against a Plzen side that played physical football throughout the match.
"We are happy, because we knew we couldn't underestimate our opponents and we didn't," Inzaghi said.
"The boys were good. They remained focused and I congratulated them in the changing room after the final whistle."
After losing 2-0 to Bayern Munich in their opening match, Inter moved to three points, while Plzen remain pointless after their opening two games.