Bohannon shared a partnership of 117 with Steven Croft (47) to steer the Red Rose to 192 for five at stumps after losing both openers to controversial lbw decisions as they chased an awkward target of 278 at Wantage Road.
Keaton Jennings and Luke Wells were both given out despite apparent inside edges onto the pad, but Bohannon’s solid knock tilted the contest back in the visitors’ favour until a cluster of late wickets, with Ben Sanderson claiming two of them, gave Northants renewed hope.
Earlier, Ryan Rickelton’s unbeaten 58 had guided the County to 174 in their second innings, with Simon Kerrigan (43) helping him to add 95 for the eighth wicket despite Will Williams’ first five-wicket return in Championship cricket.
With overcast conditions offering plenty of swing for Lancashire’s bowlers, Tom Bailey (4-65) got the fifth ball of the morning to nip back and dismiss Will Young lbw, while Luke Procter edged to first slip.
Emilio Gay weathered the storm, digging in to nudge Northamptonshire’s lead above 150, but his two-hour vigil for just 17 was ended by Luke Wood’s lethal inswinging yorker to trap him leg before.
Returning for a second spell before lunch, Bailey made deeper inroads as he castled Lewis McManus before foxing Tom Taylor with a slower ball that sent middle stump flying and left the batting side reeling at 75 for seven.
However, their fortunes were transformed after the interval as Kerrigan went for his shots and that drew Rickelton – dropped on eight by substitute wicketkeeper George Lavelle off Williams – out of his shell in turn.
While Rickelton pulled out the reverse sweep to combat Washington Sundar, Kerrigan fought a personal duel against Wood’s short-pitched bowling, taking a sharp blow on the hand but recovering to carve him over the slips for one of his six boundaries.
Lavelle put down another chance off Williams, with Kerrigan the man to escape this time, but it proved less costly for Lancashire as the next ball was snicked to first slip, where Rob Jones knocked it up for Wells to grab.
Ben Sanderson lasted just two deliveries, with Wells taking the catch again, and Williams wrapped up a well-deserved five for 41 by knocking back Jack White’s off stump to end the Northamptonshire innings for 174.
Sanderson struck in the third over of Lancashire’s chase, with Jennings hesitating after the umpire’s finger went up and there was visible frustration from Wells (26) when he suffered the same fate against Taylor after tea.
But Bohannon began to find his rhythm, particularly against the spinners, and swept Rob Keogh for three boundaries in an over as Northamptonshire rotated the bowling without reward.
Yet Sanderson kept his side in contention by capturing the wickets of Croft and Dane Vilas late in the day and nightwatchman Matt Parkinson also perished to Keogh to leave the visitors still 86 short of victory.