The former Manchester United goalkeeper did superbly well to keep out Kirk Broadfoot's header in a match of few chances at Bloomfield Road.
And his vital stop meant the Robins moved within two points of safety despite falling to the foot of the league while Blackpool are still without a goal or a win since Paul Ince's return.
It was the home side that had the first real opportunity of a quiet start in the 17th minute when Matt Phillips' cross found Matt Derbyshire but Liam Fontaine did enough to stop the former Blackburn man from testing Heaton.
The Robins, buoyed by relegation rivals Wolves' draw on Friday night, then had three half-chances in quick succession blocked by Blackpool defenders with Marvin Elliott, Lewin Nyatanga and Jon Stead all trying their luck from distance.
Stead's goalscoring ability helped City record a vital victory against Barnsley last Saturday and he was next to threaten with a looping header from the centre of the penalty area on the half hour mark which was comfortable for Matt Gilks.
It was City doing all the pushing as they looked for a crucial three points and, after heading straight at Gilks, Steven Davies had the ball in the net but the former Derby man was flagged for offside.
Blackpool carved out the best chance of the game for Broadfoot but Heaton was up to the challenge and the former Cardiff stopper did superbly well to keep out the Scot's header from Thomas Ince's corner.