The ZAZ-965 model was made between 1960 and 1969. Despite speculations that the design was copied from the Fiat 600, ZAZ representatives say the car was an exclusively Soviet design, created by Soviet ZAZ engineers jointly with colleagues from Moscow's NAMI. It was powered by a MeMZ-965, a rear-mounted, aircooled OHV 887 cc V4 engine of partially aluminium design, giving 26 hp (19.4 kW) (27 hp (20.1 kW) in the ZAZ-965A).

A common (and false) urban legend is that the Zaporozhets's engine was used as a starter motor in Soviet tanks. The base model was manufactured between 1960 and 1963, and the ZAZ-965A, which had the air-intake "ears" removed, between 1962 and 1969.

Interestingly, the engine looks a bit like the VW aircooled boxer four, except that the two cylinder banks are at a 45 degree angle. As Russian car owners were expected to do much of the servicing themselves, and auto workshops were in short supply anyway, this layout was more practical. Especially if there was four feet of snow.