The White Rose comfortably defended a target of 230 to win by 95 runs and move 14 points clear of their second-bottom opponents.
Lancashire, who have only one fixture remaining while Yorkshire have two, were bowled out for 134 within the first 40 minutes of day four. Ben Coad finished five for 24, while Jack Brooks returned nine wickets in the match.
At Trent Bridge, Indian opener Murali Vijay led Essex to their fifth championship victory, compiling a high-quality innings of exactly 100 against Nottinghamshire.
Tom Westley finished with an unbeaten 110 as the visitors, set 282 for the win, reached their target just before lunch to complete a comfortable eight-wicket victory.
Essex had began the final day in an already commanding position, at 147 for one, with Vijay resuming on 73.
In Division Two, an unbeaten half-century from Harvey Hosein and 62 from Wayne Madsen helped Derbyshire secure successive championship wins with a one-wicket victory at Northamptonshire.
The hosts had resumed on 198 for eight before Tony Palladino wrapped things up with two wickets in six deliveries, leaving a target of 233.
After reaching lunch at 85 for one, Madsen brought up his half-century before Northants hit back with four wickets for 24 runs.
However, Alex Hughes (28) and Hosein (54 not out) steadied the ship as Derbyshire prevailed.
Elsewhere, Glamorgan suffered a sixth consecutive defeat as Gloucestershire wrapped up a nine-wicket victory inside eight overs.
Opener Chris Dent hit an unbeaten 25 as Gloucestershire reached their victory target of just 35 for the loss of one wicket in Cardiff.
Glamorgan had added 16 runs to their overnight score before left-arm seamer Matt Taylor completed a five-wicket haul by bowling Michael Hogan.
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