The Magpies trailed at the interval, Alan having converted from the penalty spot after Mathieu Debuchy had fouled Felipe Pardo on the stroke of half-time.
But Coloccini pulled the hosts level on the hour mark when he connected with a corner.
The Magpies threatened early on, Hatem Ben Arfa dribbling down the left before crossing for Coloccini, whose first-time shot was only just wide.
Papiss Cisse then drew a diving save from Braga keeper Eduardo with a curler before setting Jonas Gutierrez free on the left but Shola Ameobi put the winger's cross over the bar.
And Braga surprised the home fans just before the break when captain Alan slotted home from the penalty spot after Debuchy upended the onrushing Pardo.
Newcastle went on the front foot after the break, Ameobi going close with a near-post shot that was deflected behind.
But they did not have to wait long for an equaliser, Coloccini heading home Ben Arfa's delivery to score Newcastle's first goal from a corner since Demba Ba's effort against Wolves in 2011.
Substitute Yoan Gouffran thought he had given Newcastle victory five minutes from time when he was on target from close range but his effort was ruled out for offside.