Alexandre Pato opened the scoring for Milan, who had already reached the last 16, in the 47th minute when he collected a cross from Robinho and beat Plzen goalkeeper Marek Cech.
The Brazilian pair switched roles a minute later and this time Robinho was the scorer.
But a minute from fulltime, Marek Bakos passed to an unmarked David Bystron who revived Plzen's chances for a point.
Prague's Eden Stadium went crazy when Marian Cisovsky lobbed the ball to substitute Michal Duris, who beat Milan goalkeeper Marco Amelia three minutes into injury time.
"We mainly blew the first half. We did not really let Milan do anything, we had about four chances," said jubilant Plzen coach Pavel Vrba.
"Then in three minutes we conceded two goals which were both very cheap. But we showed some strong will, we wanted to show attacking football which was risky because it opened space for breakaways but it paid off."
