Luke Procter claimed a fourth career first-class five wicket haul to give his side a handsome first innings lead, though a number of late wickets stalled progress as Northamptonshire closed Day 3 92 for seven leading by 228.
Higgins took three for 26 and Tom Price two for 22 as the Glosters found a sliver of hope in a game they looked well out of.
56 from Graeme van Buuren and an extended resistance from Gloucestershire’s tail had earlier held up Northamptonshire before they were eventually bowled out for 191.
The bowlers seized upon the momentum to leave Northamptonshire in an uncomfortable position in their second innings, despite a lead in excess of 200.
Price led the charge, striking in the fourth over as Emilio Gay was unlucky to see a forward defensive roll back into his stumps. Price added Rob Keogh 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 himself well outside the line of off stump. His later spell removed Harry Gouldstone, so impressive in the first innings, for only seven when he was bowled by a ball that kept notably low.
Adam Rossington was also bowled but this time to a lovely delivery that moved sharply away off the wicket to hit off stump, Northamptonshire’s bowlers likely making note of the assistance offered by the pitch.
Ricardo Vasconcelos was also bowled having moved in the pleasant way of his to 26, but a mixture of seam movement and an inside edge saw his off stump knocked back as he looked to drive. Saif Zaib made 14 before he was squared up by Warner and edged behind.
It was slippery stuff in the gloaming and followed some frustrating resistance from the Gloucestershire tail.
Resuming 90 for six replying to 327, the home side were in danger of conceding an even more mighty 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 on the bounce through the slips for the day’s opening boundary before clipping him through midwicket and cutting Jack White through point.