Earlier, Ormskirk-born ex-Red Rose Jones posted his first century since rejoining Lancashire from Durham over the winter. He reached a 33-ball 50 and helped them to 100-1 in the 18th over.
Either side of losing George Bell lbw playing to leg against two-wicket seamer Jack White, Jones hoisted three sixes over long-on and long-off and hit one arrow straight off Ben Coad’s seam.
He later pulled successive sixes off Matthew Revis towards the latter stages of a 92-run stand with his captain Marcus Harris, who was the first of two wickets to fall in as many overs as the score fell to 136-3 in the 24th.
Harris was caught behind driving at Revis for 32 before Coad trapped Josh Bohannon lbw without scoring.
Jones reached his century off 79 balls and hit seven sixes in all. But the visitors were checked impressively through the middle of their innings.
They were limited to 40 runs from the end of the 25th over – 143-3 – to the end of the 35th, where they reached 183-4 having lost Jones slicing White out to deep cover.
Replays suggest George Balderson was reprieved on 18 as he pulled Dan Moriarty for four. Him stepping on off-stump in the process went unnoticed by the umpires.
Balderson made a dynamic 70 off 48 balls as Lancashire fell just short of 300 in excellent batting conditions.
Tom Bailey had Adam Lyth caught behind driving early in Yorkshire’s chase, which fell to 16-1.
But Luxton kicked things into life by taking three fours and six – all through leg – off Will Williams’ first four balls, in the 11th over, as the score moved to 57-1.
From there, Luxton and Imam cruised along against a Lancashire attack lacking depth, understandable with half a dozen bowlers on Hundred duty.
By the time Luxton reached his 50 off 42 balls, Yorkshire were 107-1 after 20 overs. Imam’s third in as many matches – this off 72 balls – followed shortly afterwards.
When Luxton miscued Charlie Barnard’s left-arm spin to long-on, Yorkshire were still a long way ahead at 169-2 in the 30th over.
Imam reached his latest hundred off 118 balls by pulling Bailey for his third six before falling caught at midwicket on the pull against Arav Shetty’s spin – 220-3 in the 37th.
James Wharton and Revis wrapped things up with 41 apiece in an unbroken fourth-wicket stand of 75.
Match report supplied by ECB Reporters Network, supported by Rothesay