Despite his leveller 15 minutes from time, Cambridge remain rooted to the foot of the table as relegation rivals Kidderminster Harriers and Rushden and Diamonds both won.
While Orient's hopes of making the play-offs took a knock despite Matthew Lockwood's stunning strike on 72 minutes.
Lockwood's fifth goal of the season looked like winning the game - but Bramble's leveller means the O's are still six points away from the play-off places.
Orient dominated the first half, but it was Cambridge who almost grabbed a shock lead on four minutes when veteran striker Iwan Roberts hammered an effort against the Orient bar and Shane Tudor fired the rebound over.
The home side hit back and created a string of half chances. Leading scorer Lee Steele saw an effort blocked and Andy Scott headed just over.
As the O's continued to press, Daryl McMahon saw his well placed shot pushed away by United's Everton-bound goalkeeper John Ruddy.
Orient looked to have broken the deadlock on 29 minutes when McMahon netted following an excellent through-ball from Lockwood, but his celebrations were cut short but a linesman's flag.
But United looked dangerous on the break and Tudor lobbed a shot just wide shortly before the interval.
After the break Orient went off the boil, though Gary Alexander and McMahon went close before Lockwood finally broke the deadlock with a stunning 25-yard free-kick that flew past Ruddy into the top corner.
But Orient failed to hang on to their advantage and paid the price when a corner was only half cleared to Cambridge sub Darren Quinton, who played the ball back in for Bramble to fire home from close range.