The final session of the best-of-25 match takes place at 2.30pm on Tuesday.
Trump started the evening in positive fashion as he twice closed to within one frame, but he missed a good chance to level at the mid-session interval after an error-strewn frame.
Feeling lucky? Four remarkable flukes in one day
The world No 1 missed an easy green into the corner and then failed to pot a black to win the frame, having watched an even more glaring miss from Wilson on the pink.
That put Wilson 7-5 ahead and he finished with a flourish to take control of the contest, making breaks of 94 and 80 before taking the final frame 85-47.
Kyren Wilson knocks in century during dominant evening session
Mark Selby dominated the evening session against Neil Robertson to lead 11-5 - two frames from victory.
There was only two breaks of over 50 – a 92 made by Selby in the 10th frame and 76 in the final frame – as both players struggled for fluency.
But Selby won four of the last five frames to put himself firmly on top ahead of the final session from 10am on Tuesday.
The opening frame between Selby and Robertson proved to be the longest of the tournament so far, and after almost 59 minutes it was Selby who edged in front when potting the final black.
A 73 followed from Selby, with the three-time champion needing the final black once more to take a 3-0 lead.
Neil Robertson with 'outrageous fluke' at World Championship
It was soon four when a 72 left Robertson with much to ponder at the mid-session interval, and the 2010 champion watched on as Selby made it 5-0 with a 66.
To Robertson’s relief, the Aussie got on the board with an 83, and after Selby squandered a chance in the seventh frame it was the No.2 seed who stole it to reduce the gap to 5-2.
A thrilling frame to end a gripping session saw Selby get a huge slice of luck to snooker Robertson, only for the latter - after a few misses - to get fortunate with a plant before he saw out his third frame in a row.
'Lucky boy!' - Mark Selby snookers Neil Robertson with crazy double-kiss
Meanwhile, the other morning session saw No 8 seed Wilson take a 5-3 lead over defending champion Trump.
It was a fair speedier affair than the Selby-Robertson match, with Wilson opening the encounter with a 74 before Trump hit back with breaks of 85 and 76.
Wilson then won three frames on the spin, with breaks of 72 and 79 following to hand him a two-frame advantage going into this evening’s second session.
A fluke? Kyren Wilson leaves Judd Trump stunned with bizarre pot at World Championship
Trump is no stranger to a first-session deficit, with the world number one having also trailed after his opening sessions in the first two rounds.
As he has been reminded on a daily basis, Trump is looking to end the ‘Crucible Curse’ by becoming the first first-time champion to defend his title at the Crucible.