In-form striker Scott Taylor grabbed his 17th goal of the season when he was in the right place at the right time after Danny Coid saw his free-kick parried by visiting keeper Steve Phillips.
City had threatened to have the match sewn up by half-time as the home goal led a charmed life.
Luke Wilkshire twice hit the woodwork for City. First of all his long range drive struck the Blackpool bar and, ten minutes later, he was unlucky again as his overhead kick clipped a post.
Blackpool could only muster two chances; striker John Murphy heading wide and Taylor denied by a superb sliding challenge by City defender Louis Carey after being put through by skipper Richie Wellens.
The second half was a different story as Blackpool came out all guns blazing and could have scored within a minute of the restart when Murphy agonizingly saw his goal bound header cleared of the line.
The Seasiders were well on top when they finally made the breakthrough, while Taylor and Wellens both had excellent chances to add to the lead, but found keeper Phillips a stubborn obstacle.
The Robins pressed for an equaliser and, deep into stoppage time, nearly snatched a point, but Lee Peacock's header from a corner bounced the wrong side of keeper Brad Jones' right hand post.
Delighted Blackpool manager Steve McMahon admitted his side had rode its luck at times.
He said: "They probably feel they deserved an equaliser. It was an excellent game between two good teams, but we are delighted to get the three points and we are steadily creeping towards the right end of the table."City manager Danny Wilson bemoaned his side's bad luck.
He said: "We played half as good as that this season and managed to win. I was delighted with the players, they did everything we wanted them to do but I was disappointed with the goal as they reacted quicker than we did."