Jagr bagged his third strike of the season in the second minute of overtime for the Stars, who fell behind early on through Ales Hemsky's goal.
Jamie Benn and Derek Roy turned the match on its head and although Justin Schultz levelled proceedings to send the match into the extra period, Jagr and the Stars would have the last laugh.
The Boston Bruins moved into sole ownership of top spot in the Eastern Conference Northeast Division after coming from behind to beat the Montreal Canadiens 2-1.
PK Subban's first goal of the season gave Montreal the lead but Tyler Seguin and David Krejci both struck in the third period to move clear of the Ottawa Senators.
Sheldon Souray, Saku Koivu and Francois Beauchemin were all on-target as the Anaheim Ducks eased past the Colorado Avalanche 3-0.