With eight straight wins and a draw from ten games, the Robins had the confidence but not the finishing power.
A tense finish with five minutes of added-on time could have seen the result swing either way but Blackpool took more out of the result. This was only their second point in five games, but it eased the pressure on caretaker managers Tony Parkes and Steve Thompson.
City did most of the pressing and probably thought a breakthrough would be easier when Blackpool lost Ian Evatt from their back four midway through the first half due to a leg injury.
It wasn't so. Alex John-Baptiste who had been having a tough time as right-back moved inside to partner the impressive Shaun Barker and his game improved 100 per cent.
Most of the threat from the home side was coming down the left flank where Michael McIndoe, ever ready to take on defenders, was flying. He found one of the best shots of the game which drew a fine save from American keeper Paul Rachubka, who has just reclaimed his place in Blackpool's goal.
For all the pressure they were under the Seasiders showed they were quite capable of raising dangerous raids around the success of Charlie Adam in midfield and the enterprise of D J Campbell, the striker on loan from Leicester City.
Brett Ormerod was close to giving the visitors the lead and home fans held their breath when he then went sprawling in the box, but referee Fred Graham produced a yellow card for diving. Ormerod did not protest.
McIndoe might have scored for City early in the second half but was off-target after accepting a great ball played in by Cole Skuse.
It signalled a spell of frenzied activity by City which saw David Vaughan clear off the line and Rachubka making a fabulous one-handed save.