Australian Robertson carried a 5-3 lead into the evening and the momentum continually shifted during an engrossing display of impressive pots, inventive safety and unexpected misses.
Wilson edged the opening frame of the second session on a respotted black and then won two of the next three to pull level at 6-6 going into the interval.
A sensational break of 126 put 2010 champion Robertson back ahead but, after Wilson subsequently came from 50-0 down to level at 7-7 and then moved into the lead for the first time, he was required to dig in to keep pace in a helter-skelter encounter which resumes on Wednesday morning.
McGill showing scoring power to lead Bingham
Anthony McGill moved to within four frames of a second successive semi-final appearance at the Betfred World Snooker Championship by hitting back to gain the upper hand on Stuart Bingham.
McGill, conqueror of defending champion Ronnie O’Sullivan in round two, registered two century breaks in a high-scoring second session en route to establishing a 9-7 overnight lead over the 2015 winner.
Resuming with the scores locked at 4-4 from Tuesday’s opening exchanges, the Scot dropped the opening two frames of the evening but swiftly recovered to impressively take five of the final six.
The 30-year-old rattled in knocks of 126, 83, 92, 130 and 75 to put himself in pole position for another last-four appearance in Sheffield, while Bingham’s 120 in frame 13 – his third ton of the match – gives him some hope of a comeback.
Selby holds advantage over Williams
Earlier in the day, Mark Selby took control of the battle of the three-time champions by establishing a 6-2 advantage over Mark Williams.
Selby won the opening two frames without conceding a point, including a superb break of 121, and led 3-1 at the mid-session interval thanks to a pot success rate of 99 per cent.
A knock of 60 from Williams – whose first pot of the match was a five-ball plant in the third frame – had reduced the deficit before the break but his opponent’s dominance continued after the restart.
Selby came from 55-6 down to take frame five and then produced breaks of 90 and 76 to make it 6-1 before Welshman Williams gave himself overnight encouragement by ending with a fine run of 111.
Tight affair as Trump and Murphy remain level
In the other match, there was nothing to separate world number one Judd Trump and Shaun Murphy as they finished the day level at 4-4.
Neither player was able to move more than one frame in front during an evenly-matched opening session at the Crucible.
Trump, winner in 2019, produced breaks of 87 and 68 either side of knocks of 80 and 79 from 2005 champion Murphy in a rapid opening to the contest.
Errors crept in as the match became slightly more scrappy after the interval, with Trump’s 105 in frame seven the highlight, before a 67 from Murphy left proceedings finely poised.
The four best-of-25 frame matches will be played to conclusions on Wednesday, with Robertson versus Wilson and the second session of Selby against Williams up first.
