The Wildcats had Rovers at arms length for much of the match, having taken command during a 10-minute spell when the visitors were reduced to 12 men, following the sin-binning of Graeme Horne for repeated infringements.
Hull KR did get within four midway through the second half, making the most of their own numerical advantage when Danny Kirmond was off the field, before Cockayne’s late trio earned the two points for the home side.
Both teams then tried to get a foothold in the game, and it took 18 minutes for the first score, moments after Horne was shown a yellow card after Rovers had been given a team warning by referee Steve Ganson.
Tim Smith took the ball over the line under the attention of three tacklers, and managed to an offload out to Paul Aiton, who burrowed his way over, and despite some doubts over whether he got the ball grounded, the try was given by the video referee.
That triggered a seven minute spell where the Wildcats racked up 18 points. First Reece Lyne touched down, and virtually straight from the kick-off, Danny Kirmond charged through the Rovers defence, and then stabbed a kick to the corner which bounced up nicely for Peter Fox to score against his former club.
As Horne returned to the field, Hull KR set about restoring some parity in the game, and new signing Cory Paterson grabbed his first Super League try, taking a smart offload from Craig Hall and producing a fine fend on Tim Smith, before forcing his way through a few tackles for a determined score.
Paterson had a hand in Rovers’ second try, which followed moments later, when he took Michael Dobson‘s quick short pass to tear through the Wakefield line, finding Craig Hall on his left shoulder to reduce arrears to 18-10 at half time.
The interval came at the right time for the home side, and they re-grouped at the start of the second half, scoring through Dean Collis off the back of two penalties.
Then came the sin-binning of Kirmond, which enabled Hull KR to get themselves right back in the match. First, Josh Hodgson spied a gap from dummy half to touch down under the sticks moments after Kirmond left the field, and Rovers perhaps should have scored when Dobson’s grubber caused mayhem in the Wildcats defence. Unfortunately for the visitors, Dale Ferguson failed to ground the ball after Frankie Mariano had flapped at it in defence.
Rovers did get their fourth try when brilliant work by Dobson on the blindside set him for a grubber kick, which David Hodgson pounced on in the corner, to leave the score at 24-20.
But Wakefield, in front of an impressive crowd of 9237 at the Rapid Solicitors Stadium, dug deep, and the impressive Tim Smith produced a fine bullet pass to give Cockayne a walk-in down the left for his first try, and ultimately the gamebreaker.
Cockayne then got a second as the Wildcats created an overlap, and his third came when Fox broke through some tired tackles in midfield, offloaded to Paul Sykes and he managed to avoid being tackled, to set up Cockayne’s third.
Elsewhere, Catalan overcame the third minute dismissal of Julian Bousquet to cruise to a 40-6 victory over Salford City Reds in Perpignan.