The visitors were desperate for a return to winning ways as they had suffered back-to-back defeats prior to the encounter.
It was the visitors who carved out the first opening inside 10 minutes, with Juraj Kucka heading wide from close range after the Inter defence were caught napping.
Parma went even closer on 24 minutes when Gervinho, who netted a brace against Juventus, rattled the frame of the goal from 12-yards out.
Inter, meanwhile, had to wait until the final 10 minutes for their first opening at goal, with Mauro Icardi firing over the crossbar after some good work by Ivan Perisic.
After a quiet start to the second half, Icardi was handed another chance to break the deadlock after the hour but he failed to slot home point-blank range.
Inter eventually broke the deadlock in the 79th minute as Martinez showed good strength to hold off a marker before blasting the ball into the back of the net.
The visitors managed to see off a late surge from Parma to hold on for the victory, which cements third spot for another weekend.
Fiorentina 0-0 Napoli