On-loan Blackburn man Steven Reid grabbed the only goal of the game, his first for the Black Country club, midway through the first half to secure a fifth-successive win which all but guarantees Albion at least a play-off place come May - and their longest winning sequence since 2004's promotion-winning campaign.
The Baggies dominated the opening 45 minutes and should have been more than one goal to the good at the break as Robert Koren's effort appeared to cross the line but was not given.
But, in a game of two contrasting halves, the visitors wasted a plethora of chances to draw level - Jonathan Stead the most guilty when he somehow sent the ball wide with the goal at his mercy, while Clinton Morrison went close with virtually the last kick of the game.
The result leaves the Baggies two points behind leaders Newcastle, who have a game in hand, while Coventry, now winless in four, are eight points behind sixth-placed Cardiff with seven games remaining.
Sky Blues boss Chris Coleman looked to combat Albion's threat by matching their 4-5-1 formation.
But it was the hosts who were the more dangerous in the early stages, Chris Brunt's left-wing cross almost deceiving Keiren Westwood before Ben Watson narrowly failed to connect with Joe Mattock's ball into the box from the same flank.
Coventry's threat in the opening 20 minutes mainly came via set-pieces and it was no surprise when it was the home faithful who were celebrating the game's opener midway through the first half.
Brunt's corner eluded everyone in the six-yard box, including the onrushing Abdoulaye Meite, and Reid was on hand amid a host of bodies at the back post to lash home from close range.
As the half wore on, Carson became a mere spectator between the posts for Albion despite the visitors enjoying their fair share of possession in the middle third.
And the lack of a real threat in attack must have been playing on Coleman's mind as half-time approached.
The half's controversial moment came just minutes before the interval as Koren appeared to send Graham Dorrans' free-kick over the line but, with the best efforts of Westwood to keep it out, the referee's assistant opted not to raise his flag.
Five minutes after the restart and the Republic of Ireland stopper again kept his side in the game, producing a fine diving reaction save after Koren's effort had taken a hefty deflection.
But Coventry were now providing more of a threat at the other end and they should have been level just after the hour mark but an unmarked Stead somehow diverted Sammy Clingan's inswinging free-kick wide from six yards.
Carl Baker then saw his deep ball sent back across the face of goal and avoid everyone, before failing the pull the trigger himself with another chance.
Substitute Morrison then almost snatched a point at the death but West Brom hung on to secure their eighth-successive victory at The Hawthorns and keep themselves firmly in the driving seat for an immediate return to the Barclays Premier League.