Surrey 72 (Barker 4-24) and 6 for 2 trail Hampshire 488 by 410 runs
Hampshire will hope rain can stay away from the Ageas Bowl on day four of the LV = County Championship clash as they push for a crucial victory over Surrey.
Showers over Southampton kept the players off the field until 5pm, but Surrey, who resumed on 42 for 4, ended a truncated day on 6 for 2 having followed-on after being bundled out for 72 in response to Hampshire's 488.
The visitors trail by 410 runs after the Hampshire bowlers ran amok with Brad Wheal striking with the last ball of the day to dismiss England opener Rory Burns for a duck after Keith Barker had dismissed Mark Stoneman - leaving nightwatchman Amar Virdi at the crease when play resumes on Wednesday.
Two scheduled restarts had earlier been scuppered due to brief but heavy downpours that drenched the outfield. But Hampshire more than made up for that lost time as Surrey lost 6 for 30 in just under an hour and were immediately sent back into bat again by stand-in skipper Kyle Abbott.
The hosts will be without captain James Vince for the rest of the match after he and Surrey allrounder Will Jacks were sent to Cardiff to join up with England's makeshift ODI squad to play Pakistan owing to a Covid-19 outbreak. Vince has been replaced by 18-year-old batting prodigy Tom Prest who makes his first-class debut.
Abbott struck in the fifth over after the restart with a ball that nipped back and pinned debutant Ben Geddes, who replaced Jacks, on his crease to be lbw for four.
Hashim Amla, a double centurion when the sides met at The Kia Oval in May, then fell to a peach of a delivery from Barker, who finished with 4 for 21, that uprooted his leg stump with the former South Africa Test batter top-scoring with 29.
Jordan Clark and Rikki Clarke were both dismissed cheaply by Wheal with Abbott striking again to trap Jamie Overton lbw for four. Abbott then wrapped up the innings when he diverted a Kyle Jamieson shot onto the stumps of Virdi, leaving Surrey well short of a batting point.
Victory for Hampshire, who sit third in Group Two will greatly enhance their hopes of a top-two finish ahead next week's meeting with second-placed Gloucestershire at Cheltenham. Surrey's, meanwhile, are hanging by a thread.