Thompson hit an NBA post-season record 11 three-pointers as part of a 41-point haul in the Warriors’ 108-101 victory on Saturday.
Curry finished with 29 points, 10 rebounds and nine assists.
Draymond Green had a double-double of 14 points and 12 rebounds in the comeback win for the defending champions.
The victory at the Chesapeake Energy Arena saw the Warriors level the Western Conference finals at 3-3.
The Cleveland Cavaliers await the winner of Monday’s game seven at the Oracle Arena in the NBA Finals.
Russell Westbrook (28 points, 11 assists) and Kevin Durant (29) had put the Thunder in control and on track in game six.
However, they were outscored 33-18 in the fourth quarter in front of their home crowd.
Thompson drilled his 11th three-pointer to put the Warriors ahead with just over 90 seconds remaining and Curry stretched that lead to seal the win.