The Tangerines, who completed a deal for ex-Newcastle United forward Nile Ranger hours before kick-off, threatened to take the lead when another summer recruit, Nathan Delfouneso, went close.
Jordan Rhodes was also within inches of giving Rovers an early advantage, but was thwarted by Joe Lewis in the Blackpool net.
However, Jose Riga's side were trailing by the 26th minute when Gestede found space before rifling a right foot shot into the bottom corner.
Rovers looked to have put the three points beyond the reach of the Seasiders in the early moments of the second half when Gestede rose highest to nod home Craig Conway's cross, but Blackpool managed to pull a goal back through Tomas Cywka on 53 minutes.
The result leaves the Tangerines with only one victory in 11 Championship games.