They also collected only their second clean sheet of the season in the process but are still searching for their first win under the control of Robson having collected only four points from his ten games in charge.
Robson's side had to soak up some intense Newcastle pressure during the game and things could have been a lot different if United had not been without three injured strikers - Alan Shearer, Patrick Kluivert and Craig Bellamy.
That left Shola Ameobi operating as a lone striker with Lee Bowyer and Kieron Dyer posing a threat from midfield.
Newcastle, who had returned to winning ways by beating Birmingham City on Saturday to record their first victory in eight games, had enough chances to have won the game comfortably.
But they were let down by a lack of clinical finishing. They were also frustrated by some dogged Albion defending in which skipper Darren Purse was outstanding.
The Baggies were forced to withstand an early Newcastle storm when United should really have taken a stranglehold on the match.
But the combination of their poor finishing, last-ditch defending by Purse and his team-mates and the form of Albion goalkeeper Russell Hoult kept them at bay.
It was a combination that set the tone for the entire match. Hoult denied Titus Bramble in the fifth minute after the central defender had met a Laurent Robert free-kick with a powerful close-range header.
Lee Bowyer then volleyed over the bar before Hoult frustrated Ameobi with a smart tenth minute save.
Albion's only real threat in the opening period came when Newcastle goalkeeper Shay Given spilled a long-range 13th minute drive from Ronnie Wallwork after good build-up play by Neil Clement and Robert Earnshaw. Kanu then headed the loose ball wide of goal much to the relief of Given.
But it was Newcastle who carried the more consistent threat in attack and Albion had a double let-off in the 22nd minute.
Ameobi picked out Bowyer with a neat pass and the former England international midfielder drilled in a low 30-yard drive that beat Hoult only to crash off the foot of the post.
The rebound flew straight to Robert but he could not beat Hoult who recovered his ground to save the Frenchman's shot at the near post.
Newcastle's failings in front of goal should really have been punished ten minutes into the second half.
But Albion striker Geoff Horsfield proved as ineffective as his Newcastle counterparts. Horsfield found himself with only Given to beat from ten yards after being released by a header from Andy Johnson.
But Given was able to comfortably deal with his misplaced shot. The miss did, however, spark lowly Albion into their best spell of the match and Given again had to be alert in the 67th minute when he held a volley from Earnshaw following a left-wing cross from Paul Robinson.
But in the end both sides had to be content with just a point - a result that neither team will be particularly happy with.