Murphy came flying out of the blocks in this last 16 clash with an assured break of 45 on his way to a one-sided first frame of the evening session.
But a dogged Dott squared the match at 9-9, clinching a scrappy frame on the blue. Dott moved ahead for the first time in the frame with an opportunistic break of 62 after Murphy had started the frame well.
But Murphy steadied the ship with a silky 64 to tie the game at 10-10.
A dramatic 21st frame followed as, with the pink and black remaining, Dott missed the double into the middle pocket and Murphy sunk it. But the 2005 champion was unable to finish the frame off and Dott dropped the black to force a re-spotted black. But a dreadful opening shot by Dott saw the black finish over the top corner pocket, and Murphy made no mistake to move 11-10 ahead.
That frame proved the turning point as a renewed Murphy clinched the next one to steam ahead to the brink of victory at 12-10.
Dott pegged him back with a battling finish to make it 12-11, but a missed red proved fatal for Dott as Murphy triumphed in a match that will live long in the memory.
FIRST SESSION REPORT
Graeme Dott sparked to level his World Championship last 16 match with Shaun Murphy at 8-8 after play had to be bizzarrely halted because the man dubbed the 'pocket dynamo' was suffering from static shocks at the table.
Trailing 6-2 from yesterday afternoon's opening session, Dott worked his way back to 6-4 by snaring the first two frames of the day boosted by a run of 62 in the ninth frame.
He lost a close 11th frame before complaining to the match officials that he was experiencing static shocks when placing his hand on the table.
"Graeme pointed out to referee Brendan Moore at the end of the 11th frame that he had been feeling static shocks," explained assistant tournament director Martin Clark.
"There are steel blocks on the cushions and especially if Graeme had any metal in his shoes that may have caused it. We called the players in for the mid-session interval a frame early and sprayed the carpet with water, and that stopped the shocks."
As the players departed a frame early for their mid-session interval with Murphy leading 7-4, the carpet around the match table at the Crucible was doused in water after Dott's complaints (watch the video below).
The 2006 world champion returned from the early break in fine fashion as he collected four out of the next five frames to end the second session level at 8-8 before they play to a finish from 7pm (BST) this evening.
Murphy cut a bamboozled character for much of the morning session as Dott arguably unearthed the levels of form that carried him to the title in 2006. It was also perhaps his best form of the season.
It comes at the right time with the first man to 13 frames securing a spot in the last eight against Judd Trump or Marco Fu.
Gritty runs of 59, 61 and 56 saw Dott level at 7-7 after Murphy's 65 had given him the platform for a three-frame advantage. The final two frames of the session were shared.
Dott may even feel slightly bemused he did not have a lead after having chance in both frames, but it was a safety error by Murphy in the 16th frame that earned Dott his chance to restore party after the Englishman saw a white drop in a middle pocket playing safe off the green.
Dott slotted green, brown, blue and pink to leave matters finely poised ahead of tonight's action.
FIRST SESSION REPORT
Graeme Dott trails Shaun Murphy 6-2 in the last 16 as Scotland face being without a World Championship quarter-finalist for the first time since 1988.
With four-times world champion John Higgins, Stephen Maguire and Alan McManus all out of the tournament in the first round, Dott - the 2006 world champion - is the only man from Scotland who remains active in this year's tournament at Sheffield's Crucible Theatre.
But his participation in the event is in some doubt after Murphy produced two centuries in dominating the opening session against the Larkhall man, who made several errors among the balls.
Dott benefited from a fluke on his way to restoring parity at 1-1 with 77 after losing a mediocre opening frame, but watched as runs of 128, 112, 54 and 99 left Murphy firmly in control as he pursues a second world title to go with his 2005 success.
They resume their second session at 10am on Friday morning.