The striker was teed-up from a superb back-heel by substitute Gareth Taylor and ran through to take the ball past goalkeeper Kelvin Davis and put the ball into the empty net.
Southampton have not tasted victory at home since a win over Norwich in September, but it was them who started the game more brightly.
Bradley Wright-Phillips had a right-footed shot that went just wide of the right-hand post on seven minutes after being set up by a cross by midfielder Lee Holmes.
Doncaster hit back within a minute and the Saints were grateful to goalkeeper Davis, who pulled off a superb double save.
The shot-stopper saved an effort from 12 yards from Lewis Guy, before Sam Hird's follow up which he kicked past the post.
Veteran goalkeeper Neil Sullivan then denied Andrew Surman, who latched on to Holmes' pass before seeing his shot saved by the keeper from 20 yards.
Doncaster opened the second half with a goal inside the first 13 seconds.
Coppinger beat three players on a mazy run before his shot was deflected by Wright-Phillips straight to the feet of Martin Woods.
Midfielder Woods smashed the ball into the unguarded net for his second goal of the season.
The 15,000 Southampton fans in the ground turned on chairman Rupert Lowe as boos ran out across the ground and it was Doncaster who capitalised on this and went on to grab a second from Coppinger.
Striker Marek Saganowski hit his first goal of the season for Southampton after being teed-up by Adam Lallana in injury time, but it was too little, too late for Saints.
Wright-Phillips had a chance of a shot deep into injury time but his effort went well wide of the left-hand post and Doncaster clung on to clinch a deserved victory.