Josh Magennis struck early for the Tigers with a fine volley, before Lewis Monstma equalised for the Imps after the break.
The Dutch defender turned villain seven minutes from time, however, as his clumsy challenge on Tom Eaves in the penalty area gave Wilks the perfect opportunity to win it from the spot.
Story of the match
The game's first chance arrived as early as the second minute when Josh Magennis headed over from George Honeyman's free kick.
Two minutes later, however, Magennis beat Lincoln goalkeeper Alex Palmer as he connected acrobatically with Lewie Coyle's cross to volley the Tigers in front.
Keane Lewis-Potter earned Hull a free kick in a decent position in the 30th minute, but he fired the subsequent free kick straight into the wall.
A minute later Lincoln carved out their first chance following a sweeping move on the left, which culminated in Tayo Edun crossing for Conor McGrandles, but his shot was too tame to truly test Matt Ingram.
Ten minutes before the break, Mallik Wilks capitalised on an Edun slip and made his way goalwards, before seeing his low shot well kept out and turned behind by Palmer.
As the half drew to a close Magennis went down in the Imps' penalty area under the challenge of Lewis Montsma, but the referee waved play on.
There was still time for Lincoln to go close to an equaliser, however, when in the fifth minute of stoppage time Morgan Rogers' goalbound strike cannoned off teammate Callum Morton, before Brennan Johnson's follow up was blocked brilliantly by defender Coyle.
The visitors were forced into a change for the second half as Reece Burke replaced the injured, influential Honeyman.
Lincoln looked the brighter as play resumed and were virtually camped in Hull's half for 20 minutes, but couldn't find a way through.
The Tigers looked for an immediate response and went close to regaining the lead, only for Wilks' fizzing drive to be parried away by Palmer.
Wilks earned a free kick in a good position ten minutes from time and then saw a shot deflect over from Callum Elder's free kick.
Three minutes later Montsma gifted the Tigers a penalty after pushing substitute Tom Eaves in the area. Wilks stepped up and coolly rolled the ball home sending Palmer the wrong way.
Another sub, Gavin Whyte, almost wrapped things up in the 86th minute after he was played in by Wilks, but his shot was just kept out by the outstretched Palmer's studs.
Johnson almost spoiled the party with 90 minutes on the clock, but after a weaving run, his shot hit the foot of the post with Ingram beaten, but rebounded wide.
Takeaways from the match
Hull Championship bound
The Tigers were somewhat fortunate to win late on at the LNER Stadium, but you can't take anything from Grant McCann's side who have put together a superb 13-game unbeaten run at the business end of the season.
The Imps, meanwhile, look well placed for the play-offs after Blackpool and Charlton Athletic’s failures to win left Michael Appleton's side with a four point cushion from seventh placed Portsmouth - and with a game in hand.
George Honeyman was at the heart of all Hull's best play before being substituted through injury at half time.
Josh Magennis, meanwhile, proved a constant menace and bagged his 18th goal of the season early on.