Glamorgan 351 (Wagg 83, Meschede 78, Claydon 5-106) and 22 for 0 lead Kent 282 (Dickson 75, Rouse 65, van der Gugten 5-79) by 91 runs
Kent were in danger of trailing by a substantial margin on the first innings after losing half their side for 85, but Sean Dickson and Adam Rouse with two determined half-centuries guided them to a respectable total to reduce Glamorgan's chances of forcing victory.
Rouse's resistance did not come without incident as he dislocated his finger for the second successive day.
Glamorgan extended their first innings lead to 91 but with an uncertain weather forecast for the final day, there is unlikely to be a positive outcome to the game, especially after 104.5 overs were lost on the first two days.
Resuming on 10 for 0, Kent lost Daniel Bell-Drummond to the first ball of the day when he nicked one from Timm van de Gugten to Jacques Rudolph at slip who then parried the ball to Will Bragg alongside him.
Joe Denly then played inside a ball from the Netherlands seamer, and when Sam Northeast wafted at a delivery from Graham Wagg, Kent had slumped to 55 for 3.
Tom Latham looked in impressive form with five fluent boundaries, but the New Zealand opener then shouldered arms to Wagg, completely misjudged the line and was bowled.
Darren Stevens played a rash stroke 10 minutes before lunch, before Dickson and Rouse began to rebuild the innings.
The pair put on 72 before Rouse dislocated his finger again and retired hurt, but Calum Haggett proved an adequate replacement as he helped Dickson add a further 48.
Dickson, who faced 104 balls and struck a six and six fours in his 75, was dismissed attempting to guide van der Gugten over the slips, before Haggett was out in the last over before tea.
Van der Gugten ended with career-best figures of 5 for 79, his second five-wicket haul of the season and his first-class career, his achievement coming n successive games.
Michael Hogan's exemplary control was reflected by his figures of 19-8-24-2.
Glamorgan had 11 overs to bat at the end of the day, with Rudolph and Wallace, who have been short of runs this season, making a cautious start against the new ball.
Van der Gugten said afterwards: "I was delighted with my performance and my second five-wicket haul for the side. The pitch is a good one with plenty of carry and I have enjoyed bowling on it."