The Capitals tied it 1-1 at 13:18 of the third period when Schultz's shot hit Evgeny Kuznetsov near the net and Ovechkin knocked in the puck from the slot.
"Sometimes you have to get those really gritty ones," Ovechkin said. "It's still the same whether it's a goal from my spot [left circle], or whatever. It's [a] most important goal and I'll take it."
Ovechkin made it 2-1 at 16:27 when he scored in front off the rebound of John Carlson's shot.
"[Ovechkin] goes to the hard areas and that proves it right there," Capitals coach Peter Laviolette said. "I thought we did a better job of finding pucks that actually got through to the net in the third period, and he was in the right position. That was where he was supposed to be."
Panarin gave the Rangers a 1-0 lead with a power-play goal at 16:42 of the first period. After Adam Fox hit the post, Ryan Strome got the rebound in the right circle and passed across to Panarin, whose one-timer from the right circle deflected in off Vanecek.
Panarin has three goals and four assists in four games since missing nine games during a leave of absence.
"We had some breakdowns down low. A couple of rebounds in front in the last five minutes," Rangers defenseman Jacob Trouba said. "It's tough to lose that way, but I don't think we're looking at that. We're looking at the good things we did for 55 minutes of that game."
NOTES:Ovechkin has scored 115 game-winning goals, three behind Phil Esposito for third in NHL history behind Jaromir Jagr (135) and Gordie Howe (121). … Ovechkin tied Howe for fourth in NHL history with 147 multigoal games. He trails Wayne Gretzky (189), Brett Hull (158) and Mario Lemieux (154). … Carlson (393 assists) passed Mike Gartner for fourth in Capitals history behind Nicklas Backstrom (705), Ovechkin (583) and Michal Pivonka (418). … Washington's Zdeno Chara turned 44 on Thursday. He joins Chris Chelios, Doug Harvey and Tim Horton as the NHL defensemen to play at 44 or older. … Kuznetsov has scored seven points (one goal, six assists) in a six-game point streak. … Rangers forward Brendan Smith played his 500th NHL game. … The Rangers streak of 10 straight goals ended. It was their longest over a span of multiple games since they scored 10 from April 18-19, 2013. … The Rangers held the Capitals to 18 shots on goal, tying their season low (March 13 at the Boston Bruins).