The win extends Wanderers' late season form as they have lost only once in their last eight matches.
The defeat for the Tangerines continues their dreadful recent record with it being their 11th loss on their travels in their last 12 games.
Alex Baptiste was suspended after being sent off in the Trotters' 2-2 draw at Yeovil.
Meanwhile, the visitors were able to give a debut to veteran marksman Robert Earnshaw after he signed a loan deal from Cardiff on Friday, the striker coming off the bench after half-time.
The home side dominated attacking territory early in the game, with on-loan strike force Joe Mason and Lukas Jutkiewicz both looking lively.
They made their pressure count just over 15 minutes into the match. Jay Spearing's corner was latched on to by Wheater, whose towering header was enough to beat Matt Gilks in the Blackpool goal.
But shortly after the goal, the momentum suddenly shifted the way of the Tangerines.
From a Bolton corner, former Stoke striker Ricardo Fuller raced away down field and found Andy Halliday just outside the penalty area, but he fired his left-footed shot into the side netting.
Elliot Grandin then almost equalised when he was left free in the box, his fizzing low strike going inches wide of Adam Bogdan's goal.
Centre-back Gary Mackenzie was given the same luxury of having time on the ball in shooting range, but again he could not direct his shot on target.
However, the closest they came to levelling the scores in the first half was when Zat Knight's attempted headed back pass hit the post as Wanderers held on to the lead at the break.
The second half then started like the first ended, with the Seasiders continuing to look the more threatening.
Fuller once again managed to break down the left and cut the ball back to Grandin, although once again he failed to convert.
Trotters manager Dougie Freedman then opted to bring Jermaine Beckford off the bench for Joe Mason - a move which almost paid immediate dividends after fellow substitute Chung-Yung Lee's through ball saw the former Leeds striker come close to guiding the ball past Gilks.
Although he did not manage to hit the back of the net, the move to bring on Beckford saw Bolton start to take control of the match. His running in behind the defenders provided the threat that had ceased after Wheater opened the scoring.
The home side then saw the game out comfortably to record their third victory in their last four at the Reebok.