The hosts lost their last five wickets for 54 runs and were 333 all out in their second innings, which was wrapped up just before the close on day three.
England all-rounder Ben Stokes (3-50) broke a second-wicket stand of 114 between Procter and Haseeb Hameed when the latter was caught at slip for 53.
But Procter (122) got to three figures off 235 balls, his second ton of 2016.
The 28-year-old left-hander spent exactly six hours at the crease, although he should have been run out and was also dropped by wicketkeeper Michael Richardson before bringing up his third first-class century.
Procter was eventually caught at leg gully off leg-spinner Scott Borthwick (3-98), who took some late punishment as tail-ender Nathan Buck smashed 27 not out, including two huge sixes in an over which cost 18 runs.
The victorious team will climb up to second in Division One.
Durham's Stokes and Lancashire paceman James Anderson have been recalled by England for the second Test against Pakistan, which starts at Old Trafford on Friday
Hameed was Stokes' first scalp, the teenage opener gloving a rising short ball to substitute fielder Jeremy Benton at slip, and he returned later to remove Simon Kerrigan and Matt Parkinson.
Buck replaced Anderson, who successfully proved his fitness to the England selectors following a shoulder injury, in the Lancashire side at the start of the third day's play.
Durham all-rounder Ben Stokes: "The back's fine and the knee's fine, which is the main thing.
"It's my first game back and I've got through it - to know I can run in unrestricted and bowl overs is good."
Luke Procter's watchful century for Lancashire left Durham a final-day victory target of 247 at Southport.