The New Zealand opener dominated as the Lightning recorded 199-5 at Old Trafford on Friday evening.
Durham, out of contention with this defeat, raced to 78-0 after six overs in reply as David Bedingham made 50 off 24 deliveries.
Sean Dickson’s 53 off 33 then took their target to 15 from the last over, but Danny Lamb defended it as the visitors finished on 193-5.
A Lancashire home win over Yorkshire in their final North Group fixture on Saturday will secure their qualification for the last eight.
Allen crashed eight fours and three sixes in 28 deliveries, with his 21-ball half-century one slower than Jos Buttler’s Lightning record.
He shared 101 in 8.1 overs with former Durham batsman Keaton Jennings after Lightning captain Dane Vilas had won the toss.
Jennings (43) and Alex Davies (56) provided excellent support to give Lancashire a stronghold at the halfway mark.
Scott Borthwick, the pick of Durham’s bowlers with 2-30, had Allen caught at long-off to break the opening stand before he had Jennings caught at short fine-leg.
Durham raced out of the blocks in reply, bettering Lancashire in the powerplay by three runs.
Bedingham, like Allen, was strong down the ground while Graham Clark (37) played the support role in their 88-run opening stand.
However, the momentum swung back towards the Lightning in the space of two overs.
Clark found long-on from Steven Croft’s off-spin before Tom Hartley had Bedingham caught at short third-man, shortly followed by Cameron Bancroft’s wicket to make it 96-3.
Dickson kept the game very much alive and, by the time he had reached 40, Durham were 158-4 after 17 overs, needing 38 more.
He holed out off Luke Wood at the end of the 19th, leaving Brydon Carse and Ben Raine with a task that was just beyond them.
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