With the game pointless, England hooker Hartley lashed out at Tigers' Matt Smith with just 17 minutes gone.
Tigers registered a penalty try, but after the break Alex Waller and Ben Foden went over for the champions and Niki Goneva scored two of his own.
But with three minutes left Jamie Elliott touched down to win an epic derby at Franklin's Gardens.
It was all in spite of Saints captain Hartley's indiscretion, the latest on a growing rap sheet throughout his career which will raise questions about his credentials to represent England, regardless of whether his inevitable ban stretches into next year's Six Nations.
With two separate brawls having broken out on the pitch, replays showed that Hartley's elbow connected with Smith's chin during a scuffle, and referee JP Doyle took the advice of the television match official to send off the 28-year-old.
After missing last year's British & Irish Lions tour of Australia with an 11-week ban after being dismissed for swearing at referee Wayne Barnes in the 2013 Premiership final - also against the Tigers - Hartley, by his own admission, was in the last chance saloon when it came to his England career.
The New Zealand-born forward, who rejected a big-money move to Montpellier to sign a new Saints deal this week, can also count a 26-week ban in 2007 for eye gouging and eight-week and two-week bans in 2012, for biting and striking respectively, among his misdemeanours.
With just 17 minutes having passed when he trudged off the field, Saints, like in the 2013 final, were once again without their captain and facing an uphill battle.
Immediately after Hartley's sending off, which inevitably overshadowed a typically ferocious East Midlands derby, things got worse for Saints who, still trying to regroup, conceded a penalty try for impeding three consecutive scrums.
Owen Williams slotted the conversion and Stephen Myler put over a penalty for Saints, before Tigers' Tom Croft was sin-binned moments before the break for a high tackle.
Myler collected the points off the tee and after the interval Saints capitalised on Croft's absence, pinning Tigers back into their 22 and freeing up Salesi Ma'afu to pass on to Waller for the score.
Tom Youngs, who may be eyeing up Hartley's place in Stuart Lancaster's England side, lasted less than 50 minutes as he continued his return from injury, but Tigers were able to reassert themselves when they were back up to their full quota.
Replacement Freddie Burns's break down the middle had Saints scrambling under their posts and Leicester quickly recycled as Goneva crossed after taking a pass from Williams, who skewed his conversion wide.
Fourteen-man Saints once again validated their status as champions and Premiership leaders, though, when Luther Burrell, who was a powerhouse all afternoon, burst forward, allowing the ball to go through the hands to Foden for a superb finish from 35 metres.
It looked like it might be to no avail as Tigers, unbeaten in four Premiership games coming into the match, turned it over in midfield through Julian Salvi and put Goneva over in the corner.
But, remarkably, Saints found time for one more push and, from a line-out, swept the ball across the pitch for Elliott to clinch an unlikely and thrilling victory.
Northampton Saints director of rugby Jim Mallinder:
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"At half-time Tom Wood said 'let's do it for Dylan'.
"It was a tremendous, spirited performance. Not just relying on spirit and guts but also a lot of technical and tactical work.
"In terms of the red card it is disappointing. Dylan has to keep his arms down but he's being held and I don't think there is any malice in it. The nature of the game didn't justify a red card. I think Smith went down pretty easily, which was disappointing.
"I think the referee's initial decision of a yellow card would have been the correct decision.
"I thought Luther Burrell was outstanding. After 20 minutes we said we were still going to take them on and what we needed from Luther was to stay strong and on his feet and he did that brilliantly."
Leicester Tigers director of rugby Richard Cockerill:
"I'm frustrated with how we managed that second half. We got what we deserved. You have to control that field position and get that forward pack into the right areas of the field so we can have opportunities to create attacks.
"We were defensively poor. We were too narrow. It will be interesting on Monday morning when we look back and see a side with one less back creating opportunities.
"Saints outplayed us. They took advantage of our naivety in defence. We seemed to go AWOL at times in defence."
Northampton Saints: Wilson; K. Pisi, Stephenson, Burrell, North; Myler, Fotuali'i; A Waller, Hartley (capt), Ma'afu; Lawes, Day; Clark, Wood, Manoa.
Replacements: Haywood, E. Waller, Denman, Dickinson, Dowson, Dickson, Elliott, Foden.
Sent Off: Hartley (17).
Leicester Tigers: Tait; Scully, Smith, Allen, Goneva; Williams, B Youngs (capt); Ayerza, T Youngs, Cole, Kitchener, Parling; Croft, Salvi, Crane.
Replacements: Ghiraldini, Rizzo, Balmain, De Chaves, Barbieri, Harrison, Burns, Benjamin.
Sin Bin: Croft (39).
Att: 13,591
Ref: JP Doyle (RFU).
Dylan Hartley was sent off in the first half but Northampton edged to victory over East Midlands rivals Leicester.