The Bees are chasing a play-off spot - but will have to start converting their chances if they want the chance to make the jump in to the Championship.
Martin Allen's side dominated the game from the start and had two good early chances to take the lead.
After just two minutes the Bees won a free-kick on the right side of the penalty area. Midfielder Steve Hunt sent a teasing left-footed cross into the penalty area which Sam Sodje met with a header that flew just wide of the Peterborough upright.
Brentford kept up the pressure and five minutes later were only denied an opener by Posh goalkeeper Mark Tyler. Hunt thought he had scored as he struck a superb volley from the edge of the area, but Tyler managed to tip his drive over the crossbar.
The game began to turn scrappy as neither side managed to take control of the midfield area and it was the visitors who eventually carved out the next chance of the game.
On 37 minutes a long throw by Andy Legg was headed away by Ed Hutchinson, but Peterborough captain Curtis Woodhouse sent an 18-yard volley straight back at the Brentford goal only to see his effort whistle over the bar.
Kevin O'Connor hit a left-footed shot well wide of the Posh goal in the dying minutes of the first half, and the teams headed in on even terms at the break.
Darren Pratley was looking sharp in midfield and almost broke the deadlock five minutes into the second period. He was set up by Scott Fitzgerald 20 yards from goal, but his strike was deflected just wide of the Peterborough goal.
Three minutes later the ball was in the net - but referee Paul Danson ruled it out for offside. Isaiah Rankin's cross was turned into his own net by Christopher Kanu, but the visitors were relieved to see an offside flag raised on the far side.
A double substitution by United boss Barry Fry on 58 minutes saw forwards Wayne Purser and Fola Onibuje introduced to the game in a desperate attempt to snatch three points for the struggling visitors.
But it was the home side that came closest to grabbing a winner as Rankin had a shot cleared off the line by Mark Arber on 67 minutes. And Arber was the hero again in the dying minutes as he cleared a Sodje effort off the line.