Sharks were the stronger side in the first half, Dwayne Peel putting the visitors ahead after just four minutes.
Irish upped the attack to get back into the game, but a penalty, try and conversion from Danny Cipriani gave Sale a 18-10 lead at half-time.
The Exiles looked sharp after the break as they looked to overturn the deficit.
George Skivington scored his first try for Irish to cut Sharks lead to four points.
Charlie Amesbury scored a consolation for Sale in final seconds of the game.