Both sides put on a classy passing display but clear-cut chances were few and far between, though Eric Black's men dominated the second half against the league leaders.
Just as the game looked set for a stalemate, Patrick Suffo laid the ball on for Jackson, who finished calmly having only been on the field for 30 seconds.
Albion had spurned two gilt-edged chances in the opening ten minutes and both fell to Rob Hulse following errors from City defender Calum Davenport.
The first, after four minutes, saw Davenport fail to clear a cross by Paul Robinson, laying it straight into Hulse's path but the striker blazed over from 12 yards.
Then Davenport failed to track the former Crewe striker's run as Robinson whipped in another cross but Hulse's header flew narrowly over.
Coventry had a good shout for handball turned down on 25 minutes when Stephen Warnock's shot was charged down by Sean Gregan.
Gregan was involved again when he looked to have tripped Youssef Safri on the edge of the box but referee Neale Barry booked the Moroccan for diving.
Julian Joachim then came within inches of handing City the lead as he broke through but his finish from a tight angle was glanced wide by Russell Hoult.
Coventry's outstanding keeper Gavin Ward had the last say of the first half, diving well to block a Hulse effort.
Ward was called into action again after the break when Jason Koumas weaved through the Coventry defence and laid on Bernt Haas, but the wing back should have done better as Ward tipped his shot over.
A late Koumas free kick after the Welsh midfielder was fouled by Safri drifted wide of the upright before Jackson's dramatic heroics.