The win sees New York (13-18) pull within one game of the Washington Mystics (14-16) for the fourth and final post-season spot in the Eastern Conference.
In the fourth quarter, All-Star Deanna Nolan's 15-footer helped Detroit grab an 84-78 advantage at the 2:12 mark.
However, the Liberty refused to throw in the towel as Ashley Battle drained a three-pointer and Catherine Kraayeveld scored on a layup to draw within 84-83 with 41 seconds to go.
After two failed inbounds plays, Thorn received a pass with three seconds left and fired an off-balanced shot that bounced on the rim before falling in at the horn.
Tiffany Jackson lead the charge with 16 points off the bench while Thorn netted 13 for New York.
Nolan scored 19 points and Katie Feenstra collected 16 and 13 rebounds for Eastern Conference leaders Detroit.
Washington came unstuck in their game against Sacramento as Nicole Powell scored 28 points to see the Monarchs to an 86-82 victory in overtime.
Powell scored 17 of her points in the second half as Sacramento turned around a 34-31 half-time deficit into a 54-43 lead at the 2:14 mark of the third quarter.
Washington's Alana Beard responded with nine of her 25 points between that time and the end of regulation, helping the Mystics send the game into overtime when Monique Currie made one of two free throws.
Powell, who scored seven points in overtime, and Scholanda Robinson shared the scoring burden in the extra period.
Robinson hit three free throws down the stretch and scored all eight of her points from the line despite not attempting a field goal.
In Sunday's other game, LaToya Thomas scored 23 points to lead the Los Angeles Sparks to an 89-80 victory over the Minnesota Lynx in the battle of the two worst teams in the league.
Thomas did her part to snap the Sparks' five-game skid, scoring 13 of her points in the second half and helping Los Angeles hold off Minnesota's second-half rally.
Trailing 41-27 to begin the second half, the Lynx were able to trim the deficit to 58-56 on Simone Augustus' jumper with 16 seconds left in the third quarter.
However, Minnesota could get no closer, giving Los Angeles a rare wire-to-wire victory in what has been a down season.
Augustus led all scorers with 28 for the Lynx, who lost for the third time in four contests.
Solheim Cup 2019
The Solheim Cup