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."

Argentina said dialogue and diplomacy were the only ways to promote democracy in Venezuela.
Venezuela's foreign minister said Mr Trump's words had been hostile and disrespectful and risked destablising Latin America.
Violent demonstrations since April have left more than 120 people dead.
President Nicolas Maduro's new constituent assembly - which can rewrite the constitution and could override the opposition-controlled parliament - has been widely criticised as anti-democratic.
Mercosur - which includes the region's largest economies Argentina and Brazil as well as Paraguay and Uruguay - indefinitely suspended Venezuela's membership last week.
Other Latin American countries also condemned Mr Trump's comments, including Mexico, Colombia and Peru, which said Mr Trump's threat was against UN principles.
Peru has been a fierce critic of Mr Maduro's government. On Friday Peru expelled Venezuela's ambassador after Caracas sent an "unacceptable" response to regional condemnation of its new constituent assembly.
Peruvian President Pedro Pablo Kuczynski has urged Mr Maduro to resign and called him a dictator.
On Friday evening Mr Trump told reporters the US had "many options for Venezuela, including a possible military option if necessary".
"The people are suffering and they're dying," he added.
The US recently imposed sanctions on President Maduro, branding him a dictator.
The White House later said that Mr Maduro had requested a phone call with the American president.
In response, the White House said Mr Trump would gladly speak to his Venezuelan counterpart, when democracy had been restored in the country.
The Venezuelan opposition accuses Mr Maduro of trying to cling on to power, but he says the new assembly will bring peace to the country.
Luke Procter's watchful century for Lancashire left Durham a final-day victory target of 247 at Southport.
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The South American trading bloc Mercosur has condemned President Trump for saying he was considering military action in the Venezuela crisis.