Higgins held a commanding 7-2 lead overnight in the best-of-19 clash but lost three of the first four frames as Londoner Gould took the score to 8-5.
But Higgins, the world number six, sent out a warning with the manner of his third-frame success, putting together a 127 break - the third highest of the tournament to date.
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Gould averted defeat with an 80 in the 15th frame but could not prevent the inevitable as Higgins sealed his win at the next attempt.
Ding Junhui also secured his progress, completing a 10-5 win over fellow Chinese player Zhou Yuelong.
He was unable to add to his three centuries from the previous session - which included the tournament's top two breaks, 136 and 132 - and initially saw his lead reduced from 7-2 to 7-4 after runs of 60 and 93 from Zhou.
But breaks of 67 in frame 12 and 68 in the 15th saw Ding through.
World number 48 Stuart Carrington compiled century breaks in three successive frames as he opened up a 5-4 lead over Liang Wenbo. - but he wasn't able to reproduce that form in the evening session as he bowled out 10-7.
Carrington made his charge by stringing together 124, 101 and 107 between the fifth and seventh frames for a 5-2 scoreline.
From there, Liang took the last two frames of the session to close the gap to just one before dominating in the evening to set up a clash with Ding.
Judd Trump was pegged back by Rory McLeod as the veteran came from 4-0 down to lead 5-4.
Though a huge underdog, McLeod possesses the kind of dogged game that can knock Trump out of his rhythm and so it proved after the interval, with the world number two perhaps not helped by a long and ultimately unsuccessful pursuit of a snooker to rescue the seventh frame.
Tenth seed Ali Carter will also need to produce a comeback in the final session of his clash with Graeme Dott on Wednesday morning.
Carter trailed the former world champion 4-0 and although he won three of the next five frames, he still has a tall order to progress at 6-3 down.
Tuesday's Crucible scores & schedule
John Higgins (6) 10-6 Martin Gould
Frame scores: 77-27 (55), 82-40 (50), 66-47 (65), 84-28 (76), 96-19, 57-59 (Higgins 57), 90-0 (90), 11-100 (100), 79-10 (53), 6-109 (108), 8-76, 127-1 (127), 0-86 (86), 76-1 (67) 0-80 (80), 82-34 (82)
Liang Wenbo (13) 10-7 Stuart Carrington
Frame scores: 71-0 (70), 48-47, 16-57 (55), 7-82 (63), 26-124 (124), 0-101 (101), 20-107 (107), 63-25, 81-0 (79), 75-53, 79-0 (60), 57-68 (50), 71-37 (71), 5-65, 64-21, 74-4, 69-36
Ding Junhui (4) 10-5 Zhou Yuelong
Frame scores: 121-0 (60, 57), 93-0 (54), 73-16, 136-0 (136), 0-76, 78-8 (78), 0-127 (81), 103-0 (103), 132-0 (132), 17-78 (60), 0-93 (93), 67-1 (67), 43-70, 72-24, 76-43 (68)
Judd Trump (2) v Rory McLeod (Match 16) * (McLeod leads 5-4)
Frame scores: 96-5 (55), 64-14 (54), 58-51, 73-12, 17-80 (72), 49-64, 36-67, 0-72, 0-87 (77)
Ali Carter (10) v Graeme Dott (Match 14) * (Dott leads 6-3)
Frame scores: 53-70, 55-81, 0-75, 52-67, 71-7 (53), 73-6, 38-82 (50), 76-0 (76), 1-71
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