Strikers Tom Pope and Tyrone Barnett scored as Neil Aspin’s side secured a potentially vital away victory.
Aspin brought in Danny Pugh and Marcus Harness for suspended duo James Gibbons and Cristian Montano.
Vale were put under pressure by the home side but weathered the storm for the first-half of the game. Aspin brought on striker Tyrone Barnett for Michael Tonge at the break and the switch paid dividends as Barnett opened the scoring on 52 minutes against the run of play.
Vale looked to have secured victory when Tom Pope doubled the advantage on 69 minutes but the home side applied pressure and Vale were grateful when Bennett hit the post and a Carlisle player had the follow-up cleared off the line. However, the pressure paid off on 80 minutes when Bennett did find the target.
That goal meant an anxious final ten minutes for the Valiants but Boot pulled off another fine save as the visitors held firm to seal their second League win in a row and move further away from the League Two drop zone.
Vale: Boot, Smith, Gunning, Anderson, Pugh, Worrall, Kay, Tonge (Barnett), Whitfield (Denton), Harness, Pope
Subs: Lainton, Kelly, Reeves, Turner, Forrester
Attendance: 4,090 (214 away)