The home side were two-up inside 20 minutes courtesy of a low strike from forward Ivan Trickovski and a weak long-range effort from Danish midfielder Jesper Jorgensen which Tim Krul should have saved.
But Newcastle responded excellently, producing two goals in as many minutes to conclude the scoring before the break.
£6million man Anita opened his Newcastle account in spectacular fashion, pouncing on a loose ball and hitting a sweet volley from outside the area which flew into the bottom-left of the Bruges net, which was quickly followed by a clinical finish from Ameobi inside the six-yard box, his 14th international goal.
Yohan Cabaye could have clinched a win for his team with 20 minutes to go, but luck abandoned the playmaker as his well-struck free kick cannoned off the bar.
Following the game, Magpies’ manager Alan Pardew revealed he was confident in his side’s ability despite their disastrous start to the match, and knew they would turn around the two-goal deficit.
"I wasn't too concerned. I thought we would score goals tonight, it was just important not to let any more in,” said Pardew.
"We got a great goal from Anita after a good bit of pressure and then immediately got the second before half-time, which was a bonus, really.
"We came in at half-time in a strong position and really all we did second half was just to make sure defensively we were sound, and apart from a few break-aways and a couple of set-plays, I thought we were and it was just about whether we were going to score the winner.
"They have got pace in their team, so they are always going to be a threat.
"We hit the bar and had a couple of good situations, but overall, I am delighted. Two-nil down at Bruges, it's tough.”