The Highlanders had drawn seven in a row but produced an excellent second-half display at Firhill to plunge Partick into deeper relegation trouble.
Jai Quitongo and Kris Doolan had missed decent chances for Thistle in the first half and then Inverness took control. George Oakley headed over from three yards in 51 minutes then wide from a similar distance in 62 minutes, with Walsh the supplier on both occasions.
In 64 minutes Joe Chalmers forced a great save out of Cammy Bell with a powerful free-kick and six minutes later Walsh cut in from the left and curled a right-foot shot that Bell got a hand to but could not stop from flying into the net.
Partick blew a fantastic chance to grab a point in 75 minutes. They won a penalty when Charlie Trafford handled in the box but Blair Spittal’s effort was saved by Mark Ridgers and Chalmers blocked Doolan’s follow-up.