Alan Irvine's side travelled to the KC Stadium following four consecutive defeats and wasted a great chance to end that sequence when Allan McGregor saved Dorrans' poor spot-kick after just 10 minutes.
Hull were unable to punish the midfielder by securing all three points and are back in the relegation zone after their winless run was extended to eight matches.
The sides came into the contest occupying the two positions immediately above the relegation zone and their lack of confidence was evident as goalscoring opportunities were at a premium.
West Brom head coach Alan Irvine opted to drop striker Saido Berahino to the bench after the striker failed to score in his last five league matches.
Things will get no easier for struggling Hull, as they face a daunting trip to Chelsea next weekend, while West Brom have something to build on ahead of facing local rivals Aston Villa.
Having left out Berahino, Irvine opted to employ a five-man midfield.
But lone striker Anichebe proved more than capable of causing Hull problems on his own and the former Everton frontman had two strong appeals for a penalty in the opening eight minutes.
He went down under a challenge from Michael Dawson in the first instance, only to have been adjudged to have fouled the defender first.
But there was no doubt in referee Michael Oliver's mind the next time he went down in the box, pointing to the spot after Jake Livermore had wrestled Anichebe to the ground following a smart turn.
Dorrans failed to take advantage from 12 yards however, as his poor effort was pushed away by McGregor, diving low to his left.
McGregor has now saved all three penalty kicks he has faced in the Premier League, but his latest stop failed to spark Hull into life.
Bruce made two changes to the team that earned a point at Everton in midweek, but neither of the returning Sone Aluko and Abel Hernandez could make an impact in the first half.
West Brom's extra man in midfield allowed them to dominate possession, albeit without creating anything clear-cut from open play.
That pattern of play continued into the second half, but the hosts went close after 57 minutes when Stephen Quinn met Livermore's chipped cross from the right with a diving header, only to be denied by a good save from Ben Foster.
Hull grew into the game after that chance and looked the more likely to grab a goal. Hernandez had a good opportunity, but sent his looping header just over the bar after 78 minutes.
Irvine introduced Berahino from the bench, but the seven-goal striker was by this point feeding off little service as Hull pushed forward in search of a winner but were unable to secure an elusive victory.
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