Samir Nasri then picked up the ball 25 yards from goal and hammered a shot against the crossbar with the goalkeeper beaten.
Despite looking confident on the ball, Plzen were vulnerable at the back and Nasri again missed a chance for the opening goal. Sergio Aguero ran down the right-hand side before pulling the ball back into the box. Nasri had just the keeper to beat, but put his shot wide.
Aguero scuffed an effort wide of the post after he had shown good skill to work a shooting position on the edge of the box.
Despite City's pressure, Plzen almost took an unexpected lead. Frantisek Rajtoral worked his way into the box, but with defenders closing him down, his strike across goal was missed by everyone.
However, Rajtoral was soon the villain as he handled Aguero's cross and the referee pointed to the spot. The Argentine striker took the kick himself, sending Kozacik the wrong way for 1-0.
Plzen grabbed an equaliser with just minutes of the first half remaining, however. Tomas Horava received the ball 25 yards from goal, steadied himself, and then fired a shot into Joe Hart's top corner.
The second half began with City trying to up their game and force their opponents back, and Manuel Pellegrini's side soon had their second of night.
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However, just as in the first half, Plzen refused to sit back and were rewarded with their second equaliser of the night.
Some static City defending allowed Stanislav Tecl the time to pick his spot and find the corner for 2-2.
The match then swung back in City's favour. Navas again played a key part, crossing the ball from the right for substitute Alvaro Negredo to tap in from close range.