Gould started hot with a run to 94 to claim the opening frame, going 2-1 ahead after Murphy claimed the second.
Murphy, world champion in 2005, hit 88 to square the tie at intermission but Gould continued to have the edge of the see-saw encounter, and a break of 71 put him 3-2 up.
The ‘Pinner Potter’ was even within one frame of the last-16 when he replied to Murphy’s 52 for 3-3 with a 59 which helped him go 4-3 up.
But the world number four's 118 clearance was followed by an impressive fight-back in the deciding frame to go ahead for the first time, at the most vital time, and advance to round two.
Murphy will be paired with either Matthew Stevens or David Gilbert in the round of 16.
Also into the second round is Mark Allen after the Northern Irishman shook off a slow start to take five frames on the spin and beat Ryan Day 5-2.
Welshman Day took a quick 2-0 lead with breaks of 63 and 81, but Allen was able to pull back to level terms going into the mid-session break with a knock of 69 to win frame three before taking the fourth on the final colours.
It was all Allen from there, however, as the ninth-ranked ‘Pistol’ kept his momentum going and racked up tallies of 52, 84 and 78 to set up a last-16 encounter with Robert Milkins, who saw off Mark Davis 5-3 on Monday.
The final two wild card qualifiers completed the ongoing opening round, with Chinese amateur Zhao Xintong surprisingly making short work of Andrew Higginson 5-1 to set up a Wednesday tie with Stuart Bingham.
And Ian Burns will meet Barry Hawkins that day in the first round proper after despatching Afghanistan’s Saleh Mohammad by the same score.
Tuesday results - session one
Shaun Murphy 5-4 Martin Gould
Mark Allen 5-2 Ryan Day
Wild card qualifiers
Ian Burns 5-1 Saleh Mohammad
Zhao Xintong 5-1 Andrew Higginson