The Falcons still lead the best-of-five series, two games to one, with Game 4 set for Saturday night in Manchester.
David Savard answered less than four mintues later in similar fashion as his long shot during a 4-on-3 man advantage for Springfield got past Jones to make it 1-1.
Jones (1-2) held down the fort the rest of the way, keeping the Falcons off the board in the third period despite a 10-4 edge in shots by Springfield during the final 20 minutes.
McElhinney (2-1) finished with 26 saves for the Falcons.
The Game 3 victory marked the first time in franchise history that the Monarchs won a game when facing playoff elimination (1-10).