Goals from Ivan Trickovski and Jesper Jorgensen put the home side in the box-seat but Vurnon Anita and Shola Ameobi scored before the interval to earn a point for Alan Pardew's side.
Newcastle were lacklustre in the opening exchanges, with Tim Krul fortunate Carlos Bocca could not find a crucial pass after he had charged down the goalkeeper's poor clearance.
They went behind on 14 minutes though, with Trickovski scoring his first Bruges goal after bringing down a long ball from the back before turning inside Fabricio Coloccini and hitting a low left-foot shot past Krul.
Jorgensen then doubled the home side's lead five minutes later after his shot from 22 yards crept between Krul and his post after Jorgensen had latched onto a weak defensive header from James Tavernier.
That finally appeared to spark Newcastle into life, although Sylvain Marveaux was guilty of a miskick when unmarked in the centre after Gabriel Obertan had played an inviting cross in from the left.
Shola Ameobi then saw a header tipped over the bar by home keeper Bojan Jorgacevic after Ameobi's brother Sammy had crossed from the right wing.
But the pressure finally paid off as Newcastle scored twice in three minutes to draw level before the break.
Anita scored his first goal since joining the club from Ajax as he struck a volley with the outside of his right boot that found the net from just outside the penalty area (41).
Shola Ameobi then netted the equaliser with a neat toe-poked finish past Jorgacevic after his brother had once again played him in (43).
The second half featured fewer clearcut chances, although Shola Ameobi continued to impress as he forced a couple of decent save out of the Bruges keeper.
Yohan Cabaye also hit the post from a free-kick that had Jorgacevic well beaten but it was the home side that came closest to finding a winner.
Krul was forced to save well from headers by Carl Hoefkens and Mohammed Tchite before Jorgensen went close a minute from time.
His side-footed half-volley from a corner looked destined for the top corner but it just cleared the goal and Newcastle held firm in the final few minutes.