The Red Rose county, second in Division One, boosted their chances of winning a second title in seven years by completing a maximum 24-point win by eight wickets during the fourth afternoon.
But they were left waiting to see if Somerset could do them a favour by hanging on for the draw against leaders Essex.
At worst, Lancashire will go into next week’s top-of-the-table clash between the two 36 points behind the Chelmsford side. It could be 25 if Essex fail to win this afternoon.
Tim Ambrose’s 16th career first-class century, an excellent 104 off 198 balls, at least ensured Warwickshire avoided a fifth innings defeat of 2017 as they posted a second-innings total of 344.
But, still, their sixth defeat in 10 leaves them in a perilous situation at the bottom of the table having only taken two points.
They will either be 34 or 35 points adrift of safety by the end of the day with four games remaining.
There was no play possible before lunch due to rain, but play started at 1.10pm with a minimum of 72 overs to be bowled.
The Bears started on 275 for six in their second innings, trailing by 29, with Ambrose unbeaten on 76 and Jeetan Patel 18.
The pair brought up their 50 partnership in the first over from Kyle Jarvis, who set up this win with six first-innings wickets during the opening afternoon on Monday.
Ambrose reached his ton off 156 balls in the 88th over, the third over of play, as the pair shared a stand of 86 inside 20 overs.
That partnership was ended when home captain Ryan McLaren trapped Patel lbw for 30 as the score fell to 315 for seven in the 95th over, a lead of eleven.
Jarvis then bowled Chris Wright with one that kept a touch low in the next over to leave the score at 326 for eight.
Warwickshire were helped along by the addition of five penalty runs when a Matthew Parkinson delivery beat everyone in his first over of the day, including batsman Olly Stone, and hit the helmet placed behind wicketkeeper Alex Davies.
But the leg-spinner struck in his second, the 103rd of the innings, when he had Ambrose lbw with 339 on the board, a lead of 35.
Jarvis wrapped up the innings with his eighth wicket of the match when he uprooted Ryan Sidebottom’s middle and off stumps in the next over, leaving Lancashire with 51 overs to chase their target.
Alex Davies took two boundaries off Keith Barker’s first over, but he fell lbw to the same bowling in the fifth as the score fell to 22 for one.
Haseeb Hameed launched Patel’s off-spin for six over long-on, but he was also lbw in Barker’s next over for 21 as the score fell to 35 for two.
Liam Livingstone, whose first-innings 224 was Lancashire’s standout performance of this match, finished three not out and Dane Vilas two.