The hosts deserved the points on the balance of play and chances, but the result leaves Bluebirds manager Dave Jones with much to ponder after seeing his side slump to their fourth defeat in five league games.
The Welsh side were returning to a sun-drenched Hillsborough for the first time since seeing their play-off dreams shattered in South Yorkshire on the final day of last season.
And they got off to a nightmare start when the impressive Esajas found the net for the Owls with an inch-perfect free-kick after just four minutes.
Luke Varney hit a post before Peter Whittingham levelled from the penalty spot in the 16th minute after Michael Chopra was brought down by Wednesday keeper Lee Grant. Esajas turned provider three minutes into the second half when he crossed for Varney to head home.
And after Joe Ledley saw red for a second bookable offence, Esajas claimed his second assist of the afternoon.
The Dutch winger found unmarked substitute Leon Clarke, who had already hit the woodwork, at the back post and he volleyed home to secure the points.
Wednesday wasted no time exerting their influence as Esajas, returning to the Owls' starting XI following his sterling substitute role in last week's derby defeat to Sheffield United, secured an early lead.
Varney's run was halted by Cardiff captain Mark Hudson on the edge of the penalty area and Esajas stepped up to float the set-piece over the wall, off the post and in.
The hosts were almost two goals to the good in the 12th minute as Varney's low effort rebounded off a post and out.
But from being almost out of the game, Cardiff were level just four minutes later.
Chopra latched onto a hopeful ball over the top and as he ghosted past Grant he was brought to the ground, leaving referee Michael Oliver with no option but to point to the spot.
Whittingham subsequently stepped up and fired the spot-kick into the bottom right corner.
Both sides were showing plenty of neat touches and attacking endeavour as the half continued, although Owls skipper Darren Purse was enduring an opening 45 minutes to forget against his former employers.
But, despite Chopra and Mark Kennedy both seeing goals disallowed for the Bluebirds, a lively first half drew to a close with the score level at 1-1.
Having broken the deadlock with four first-half minutes on the clock, the home side regained their advantage just three minutes into the second half.
And the manner in which Cardiff once again made life difficult for themselves would have infuriated boss Jones.
Esajas was given plenty of space on the left to float in a cross which found the unmarked Varney and his glancing header left David Marshall with no chance.
Again, in similar fashion to the first half, Wednesday hit the woodwork shortly after finding the net, Clarke this time striking a post after latching onto Adam Matthews' woefully short back pass. Bluebirds midfielder Ledley saw red in the 72nd minute for a shocking challenge on Michael Gray which brought his second yellow card.
And the game was wrapped up 10 minutes from time when Esajas set up Clarke for Wednesday's third from close range, leaving the majority of the 18,959 inside Hillsborough to hand the wide man a standing ovation upon his late substitution.
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