Higgins took three for 26 and Tom Price two for 22 as the Glosters kept themselves alive in a game they looked well out of.
An excellent 56 from Graeme van Buuren and superb resistance from Gloucestershire’s tail had earlier held up Northants to save the follow-on before the home side were eventually bowled out for 191.
The rearguard, which saw No. 10 Matt Taylor make 24 from 97 balls and Jared Warner 10 from 82 deliveries, didn't quite deliver a batting point but it certainly wrested back the initiative.
The bowlers then seized upon the momentum to leave Northants’ second innings in tatters at the end of day three.
Price led the charge, striking in the fourth over as Emilio Gay played into his stumps trying to defend.
Price added Rob Keogh palpably lbw to a full ball that nipped back.
Higgins trapped Luke Procter lbw from round the wicket – with a suspicion that the left-hander got outside the line of off stump.
His later spell removed Harry Gouldstone, so impressive in the first innings, who made only seven before playing around a straight delivery and losing his middle stump.
Skipper Adam Rossington was also bowled but this to a lovely delivery that swung away to hit off stump. He made only 18 and there will be no captain to the rescue this time for the visitors.
Ricardo Vasconcelos was also bowled. He moved in the pleasant way of his to 26 but played loosely outside off stump to one from Matt Taylor that seamed in, and Saif Zaib made 14 before he was squared up by Warner and edged behind.
It was slippery stuff in the gloom and followed some extraordinary resistance from the Gloucestershire tail.
Resuming 90 for six replying to 327, the home side were in danger of conceding a huge lead.
Zafar Gohar quickly fell to Procter for seven but the resistance began with an eighth-wicket stand of 45 between Price, who lasted 54 balls for his 16 and van Buuren.
The No. 6 resumed on 19 and edged Procter through the slips for the day’s opening boundary before clipping him through midwicket and cutting Jack White through point.
His second 50 of the summer came in 121 balls and helped give Gloucestershire a sniff of a remarkable turnaround on the final day.
Procter was the pick of a disciplined Northants attack, claiming five for 42 from 18.5 overs, while Ben Sanderson finished with three for 39 from 21 overs and Simon Kerrigan two for 14 from 13.