Kent 244 and 120 for 5 (Worrall 3-18) trail Surrey 543 for 7 dec (Sibley 150, Lawrence 112, Burns 69, Smith 58, Parkinson 5-177) by 179 runs
Surrey are closing in on an emphatic victory against Kent in the Vitality County Championship at Canterbury, after reducing the hosts to 120 for five in their second innings, a deficit of 179.
Worrall took three for 18 as the champions rattled through Kent's top order after declaring on 543 for seven.
Matt Parkinson took five wickets for Kent, but they came at a cost of 177 runs, as Surrey hit out during a punishing afternoon session for the home side, to take a first-innings lead of 299, Dom Sibley making 150, Dan Lawrence 112 and Jamie Smith a quickfire 58.
Ben Compton and Joey Evison were not out on eight and seven respectively at stumps, but with the forecast for clear skies tomorrow Kent will need something close to a miracle to escape with a draw on day four.
For a third successive day this game was played out in a bone-chilling northerly wind and it went as almost everyone in the ground knew it would, with the champions making unmolested progress through the first hour.
The landmarks ticked by. Sibley glanced Jas Singh for four through square leg to reach three figures and Lawrence tickled the same bowler for a single to reach his 50.
Sibley then flicked Evison for four to put Surrey into the lead and Lawrence drove Jack Leaning through the covers to bring up his century.
Kent opted not to take the new ball after 80 overs and Matt Parkinson vindicated the decision when he bowled Lawrence with the very next delivery.
The afternoon session was significantly livelier. Sibley had just reached his 150 when he was given out caught and bowled by Parkinson after the umpires checked the ball had carried.
Ben Foakes then made a rapid 24 from 20 balls but he was caught behind slashing at George Garrett.
Smith was on 37 when he hooked Jas Singh to square leg, but the sub fielder Fred Klaassen couldn't haul in the catch.
Smith responded with a six off Parkinson that flew on to the upper balcony of the Cowdrey stand and he reached 50 when he swept the next delivery for a single, but he fell in Parkinson's next over, the 99th, caught at long on by Arafat Bhuiyan.
Parkinson got his fourth wicket when Ryan Patel drove him to Garrett at midwicket for 30 and despite the grim match situation he till let out a scream of delight when Jordan Clark hit him to Joe Denly at the midwicket boundary, giving him his first five-wicket haul for Kent.
Surrey finally declared at tea and with Compton off the field due to a sore neck, Harry Finch opened the batting alongside Zak Crawley.
The England opener contributed just four before he edged Worrall behind to become Foakes' 300th first class victim for Surrey.
Worrall then sent Daniel Bell-Drummond's middle-stump flying for 10 and Finch went for an entertaining but brief 24 when he was lbw to Jordan Clark.
Joe Denly made 38 but then prodded Cameron Steel to Smith at mid-wicket, before Worrall had Jack Leaning caught at slip by Sibley for 24.
There were ironic cheers when Compton got off the mark after 30 balls, but if anyone can thwart Surrey on the final day it's a man who values his wicket this dearly.