Bruce has had a difficult start since he replaced Valerien Ismael in early February, with his five previous league games having yielded just one point and one goal.
But once Grant scored after 17 minutes - a goal they deserved following a pioneering start to the match - a West Brom team clearly lacking confidence was reborn.
Hull were admittedly compliant hosts and conceded a second goal after 48 minutes when Taylor Gardner-Hickman was fouled by Jacob Greaves inside the penalty area.
Grant sent goalkeeper Matt Ingram the wrong way with a cool spot-kick that essentially put the game to bed.
Thirteenth-placed West Brom still require snookers to creep into the play-offs.
And though this was not a pitch-perfect performance, Bruce - forever remembered as Hull’s greatest manager for twice gaining promotion to the Premier League - finally has momentum.
Surely inspired by last weekend’s 3-0 win at Peterborough - and keen to capitalise upon the visitors’ recent demise - the Tigers should have started with greater intent.
They were, though, strangely passive for much of the game, most notably early on when a brisk West Brom team was determined to control possession from the outset.
Bruce’s men might even have scored after 11 minutes had it not been for Ingram’s smart stop off former Hull player Conor Townsend.
Hull, poor in possession and lacking energy through the middle throughout, were not so lucky six minutes later.
Alex Mowatt’s cross from the right was inviting, yet the hosts allowed Grant too much space to score a simple goal.
Grant’s strike failed to arouse Hull from their slumber until the 28th minute when Keane Lewis-Potter’s attempt towards the left of the penalty area went over the crossbar.
Lewis-Potter at least tested goalkeeper Sam Johnstone 10 minutes later with a fierce hit from distance which was comfortably parried to safety.
Optimism might have grown amongst Hull fans at the break following that short flurry of attacking vim.
But that quickly dissipated when Grant scored from the penalty spot as West Brom began the second half in a similar vein to which they started the first.
Hull manager Shota Arveladze made changes during a scruffy second half, but they did not change the flow of the game as Johnstone had an easy afternoon in East Yorkshire.
As, too, did Bruce as the Baggies eased to a first Championship victory since January 22.
Substitute Tom Eaves had a couple of half-chances that came to nothing, but West Brom were strong in defence and never looked like conceding.
They might even have scored a third late on had Grant shown more conviction with a weak hit that was easily saved by Ingram towards the left of the six-yard box.