Bellion headed home in the 16th minute to give the Ligue 1 team victory, moving them just one point behind Newcastle, who drew 2-2 at Club Brugge.
The margin of victory could have been greater with Carlos Henrique hitting the post with their Portuguese visitors creating little of note, although they did have a late goal disallowed for offside.
While Bordeaux enjoyed the better of the opening exchanges, they had not threatened the Maritimo goal before taking the lead in the 16th minute.
Nicolas Maurice-Belay's cross from the right found Bellion in the six-yard box and he headed the ball into the bottom right of the goal.
Their opponents looked to respond immediately with Marcio Rosario's header from Sami's corner blocked by defender Henrique.
However, they were creating little of note and it was Bordeaux who looked more likely to score, Cheick Diabate twice threatening, firstly from distance before his right-footed volley was cleared by Marcio Rosario.
The hosts almost doubled their lead four minutes before half-time when Henrique's header from the centre of the area hit the post.
Given Maritimo were only one goal adrift and in reality needed something from the game, they were offering little.
Serra Olberdam, Joao Luiz and Marcio Rosario all had efforts but none that forced Cedric Carasso into anything resembling a save.
Ramos Heldon also had a shot cleared and David Simao fired in a long-range effort and they did have the ball in the net five minutes from time but Valentin Roberge was flagged offside after heading home.
Heldon's free-kick was cleared by Gregory Sertic in injury-time as Maritimo failed to force an equaliser.