Seamers Stuart Meaker and Tim Linley shared seven Glamorgan wickets to give Surrey the advantage by stumps on day three of the rain-affected LV= Division Two match at The Oval.
Meaker (4-57) and Linley (3-24) did most of the damage as Glamorgan posted 209 in reply to the Londoners' 280 all out.
There was then still time for Graham Wagg to see off both Rory Burns and Graeme Smith as the hosts reached 50-2 at stumps, however a draw remains the favourite outcome heading into the final day.
Surrey had begun this morning on 209-7 first time round, and top-scorer Zafar Ansari (74) soon fell to a fine catch behind by Mark Wallace off Michael Hogan (3-81) - one of five in the innings for the Glamorgan wicketkeeper and captain, in his 200th championship appearance.
Glamorgan's reply was quickly minus opener Gareth Rees, caught at slip by Smith off Meaker, before Stewart Walters - against his old club - and Will Bragg put on 63 for the second wicket.
Slow left-armer Ansari broke the partnership, bowling Walters, and four wickets fell for 17 runs as Meaker moved into overdrive and put himself on a hat-trick at one stage.
Jim Allenby continued his fine start to the season with a 64-ball 50 before teenager Tom Curran wrapped up the innings with his first two Champiosnhip wickets.
At the Ageas Bowl, bad weather abated at last on the south coast to allow a full day's play between Hampshire and Worcestershire at the third attempt.
Hampshire all-rounder Sean Ervine (93) and home captain Jimmy Adams (67) helped to turn 37-3 into 263 all out to collect two batting points.
Left-arm seamer Jack Shantry finished with 4- 68 for the visitors, who then reached 103-1 in a match apparently destined for a draw with bonus points still to play for on the final day.
England all-rounder Moeen Ali reached the close 27 not out, while Worcestershire captain Daryl Micthell battled to an unbeaten 44 before stumps were called.