The Australia all-rounder thrilled an Emirates Old Trafford crowd of 9,712 with 73 off 46 balls as the Lightning posted 151 for six after recovering from two for two.
Maxwell then claimed four catches - a Lancashire record - as Notts slipped from 96 for three in the 13th over to 101 for six in the 15th.
Visiting captain Dan Christian (41 not out) brought the game back into the balance with two leg-side sixes off Saqib Mahmood as the penultimate over went for 21, but James Faulkner defended 12 off the last over, taking two wickets.
Nottinghamshire finished on 148 for nine, with Lancashire winning by three runs.
Lancashire have now won five of their seven North Group fixtures, added to two no-results, and sit on 12 points, three clear of Worcestershire in second, who have only played six.
Nottinghamshire remain in the top four with three wins and three defeats from seven outings.
Former England all-rounder Samit Patel also impressed for the visitors with one for 14 from three overs of left-arm spin and 34 with the bat.
But he was one of three wickets to fall for five runs in 12 balls as spinners Matthew Parkinson and Liam Livingstone excelled.
Parkinson became the fastest Lancashire bowler to 50 T20 wickets in his 29th game and finished with three for 22 from four overs of leg-spin.
The Lightning recovered from two for two in the first over and 35 for four in the ninth to post 151 for six thanks to a superb fifth-wicket stand of 107 between Maxwell and Dane Vilas (46).
They united for 11 overs to share their county's record fifth-wicket partnership in T20 cricket.
Having been invited to bowl, Nottinghamshire made the perfect start through left-arm seamer Luke Wood, who bowled Alex Davies with the first ball of the night and then Steven Croft with the fifth.
Shortly afterwards, Livingstone was bowled trying to scoop Pakistan left-arm spinner Imad Wasim before Keaton Jennings was stumped off Patel.
That paved the way for Maxwell and experienced South African Vilas to first of all rebuild the innings by scampering singles and twos before opening up later on.
The Lightning scored 85 off the last eight overs and 60 off the final five.
Maxwell effectively utilised the reverse pull and ramp against Harry Gurney late on before he and Vilas then fell to the left-armer in the last over.
Richard Gleeson gave the hosts the ideal start when he trapped Joe Clarke lbw with the first ball of the chase, replicating Wood's early strike.
Gleeson then had Ben Duckett caught at mid-off by Maxwell off a full-toss before Alex Hales (29) miscued a sweep at the leg-spin of Parkinson to Maxwell at deep midwicket.
Notts reached halfway at 76 for three, but things started to unravel as Livingstone had Tom Moores caught at long-off by Maxwell and Wasim lbw.
Parkinson also had Patel caught at deep cover, making it 99 for five in the 14th, and Wood stumped.
Christian's late heroics came to no avail as Faulkner struck twice in two balls in the last over, including another catch for Maxwell.
