Steve Bruce's men are in the thick of the promotion race and cemented themselves in second place heading in to 2013 with this win.
Prior to Evans' 52nd-minute opener it had looked as though the one thing to have blighted Hull this season - a dismal lack of goals - would haunt them again, but once the seal was broken they did not look back.
They were ably assisted by Neil Warnock's Leeds, though, who over Christmas have gone from promotion candidates to mid-table fodder.
United had one notable effort - a Tom Lees half-chance - and with 17-goal Luciano Becchio benched, spent the game chasing shadows and were lucky to end the game with 11 men.
Their problems were clear from the off, with the three-at-the-back system employed by Warnock leaving his players confused, something illustrated as early as the fourth minute when Alan Tate's back pass fell short and Robert Koren failed to convert a one-on-one.
Leeds' disarray at the back continued and they were fortunate not to concede a seventh-minute penalty when Sone Aluko was too quick for Jason Pearce on the outside, before they had a chance of their own; Lees stabbing over as he chased up Ross McCormack's mis-hit effort from a corner.
Leeds reverted to unsavoury methods of staying in the game, with Aidy White and McCormack booked for late challenges and Michael Brown shown a yellow card for refusing to step off the field while he received treatment.
With 52 minutes gone Aluko laid on Evans' goal. His neat reverse pass put the Northern Ireland international in down the right-hand side of the box and, without a moment of hesitation he rammed a low drive across Kenny and into the bottom corner.
It was no more than Hull deserved, in fact another couple of goals would have been justified, and one arrived three minutes later as Meyler rose to head in Robbie Brady's corner at the near post.
Only the theatrics of Kenny from Brady and Koren's wasteful follow-up denied Hull a third.