Stone, Sean Monahan, Kris Versteeg and Sam Bennett scored for Calgary. Elliott made 22 saves.
"Now we have to try and win Game 4," Stone said. "Put this one behind us and move onto the next one. One at a time."
Theodore scored twice after the Ducks trailed 4-1.
He scored his first career Stanley Cup Playoff goal to make it 4-2 with 48.2 seconds remaining in the second period, and Thompson deflected Hampus Lindholm's point shot past Elliott at 11:14 of the third. Theodore scored again with 4:21 remaining in the third to make it 4-4.
"Once we started, we got one, two and the third one, I felt like they kind of played a little more back a little bit and we just took charge and stepped our game up," Theodore said. "They came out pretty hard, but I felt like once we got our game back on track we were definitely pretty strong."