In a match that swung both ways throughout, Wilson was 3-0 and 4-1 up before Neil Robertson fought back impressively to lead 5-4 and move to within a frame of victory.
However, Wilson bounced back to win the tenth and set up a deciding frame, which he won after several tense exchanges between the pair to progress to the semi-finals where he will face debutant Wu Yize on Staurday.
"It was a fantastic game and I am glad it lived up to its billing. Neil is a fantastic champion and on any other day he drifts inside the black spot and it's 6-4," Wilson told BBC Sport.
"I made a really good clearance for 5-5 and just dug it out. It was one where win or lose you are thinking there is plenty to build on for the rest of the season."
Off to a flying start
Wilson got off to a flying start with a break of 110 to take the first frame, with the 34-year-old then rattling through the next two to take a commanding 3-0 lead.
Then came a bizarre fourth frame. First Robertson touched the brown ball with his left hand when addressing a red, before Wilson found himself with the easiest pot of a black he could hope for to secure the frame, only to miss it and leave the door open for Robertson - who trailed by five time - to get back into the game.
Robertson would eventually win the frame after Wilson attempted a tough pot and missed, leaving the Australian only two frames behind his opponent at the interval rather than four.
Wilson restored his three-frame lead by winning the fifth, but from there Robertson came fighting back. He won the following three frames, which included back-to-back centuries, to level the match at four apiece. Robertson’s first century took him to outright second in the list of all-time century breaks at the Masters with 47, behind only Ronnie O’Sullivan who has 86 to his name.
Wilson had a chance early in the ninth to stem the flow, but an error when trying to get a cue ball position off the black allowed Robertson back on the table.
By the time the Australian was done, Wilson was 45 behind with 35 remaining on the table. He forced one foul out of his opponent, but then Robertson got out of jail with great control of a swerving cue ball that not only met with the red, but sank it in the corner pocket. From there Robertson put the frame out of reach of Wilson to go within one of a place in the semi-finals.
Wilson knew he needed something special in the tenth frame, and it came in the form of a red-ball pot from the cushion at the top end of the table, before going on to notch his third century break of the match to force a deciding 11th frame.
The pair traded turns at the table in the decider before Robertson made an error going for a long pot of a red, allowing Wilson to record a break of 42 which put him 38 ahead with 35 remaining.
There was one red remaining which he couldn't pot, but he was able to position his way around the table as time ran out for Robertson, with a Wilson pot of the green eventually sealing his progress to the semi-finals where he will face Wu.