The City striker's string of misses looked for a long time as though they might prove costly in the third round replay at Eastlands.
Three times Vassell burst clean through on goal only to be denied by keeper Mark Crossley as his lean spell in front of goal continued.
But Vassell's pain turned to pleasure eleven minutes into the second half when he conjured the decisive strike - only his second goal of a disappointing season.
Bernardo Corradi's intelligent flick released Vassell who powered home an unstoppable shot into the top corner to finally break the spirited resistance of the Championship club.
Though the opening half was goalless until the 44th minute it was still an absorbing contest.
Vassell had twice burst through on goal only each time to be thwarted by the legs of Crossley, while Joey Barton curled a free-kick inches wide.
Wednesday also had their moments as Marcus Tudgay and Chris Brunt both forced City keeper Nick Weaver to make decent saves.
The breakthrough came when Barton broke on the right and squared the ball for Stephen Ireland to slot home City's opening goal and only his second for the club.
Wednesday made a double half-time substitution bringing on Yoann Folly and Wade Small and within six minutes were on level terms.
Owls captain Lee Bullen equalised with a near-post header which looped over Weaver following Brunt's free-kick.
Crossley denied Vassell for a third time - again with his legs - and it was beginning to look as though it might not be City's night as the squandered openings were beginning to look expensive.
But with the fans becoming increasingly frustrated, Vassell came up with the goal which had eluded him all night.
Corradi, substitute Georgios Samaras and Ireland all ought to have scored to seal victory for City but all were unable to find the net.
And it was City's failure to see of Wednesday which enabled the visitors to remain in with a shout until the final whistle as it proved a nerve jangling final half hour in which Small and Tudgay both had clear-cut chances which could have taken the tie into extra-time.