Manager Mixu Paatelainen insists Dundee United must replicate the desire that yielded victory over Hearts if they are to have any chance of staying up.
The Finn feels Premiership bottom side United deserved their win but feared a hard-luck story beckoned before Paul Paton's winner.
"What a save that was from Neil Alexander from Edward Ofere's header [in the first half]," he said.
"We hit the post and on many other occasions were nearby."
The gap between United and second-bottom Kilmarnock has been reduced to 11 points but Paatelainen admits there is still a long way to go with his side having 12 games to play.
"It's a long road," he told BBC Scotland. "It's a one-off victory but the next match is our most important one. We believe in it but we concentrate on our next task, which is Ross County.
"But if we continue with that sort of spirit we have half a chance."
Meanwhile, Hearts head coach Robbie Neilson was critical of referee Kevin Clancy and in particular the red card shown to defender Jordan McGhee.
United substitute Henri Anier was also dismissed for two bookings, with Tuesday's Edinburgh derby likewise seeing both Neilson's side and Hibernian reduced to 10 men.
"We didn't deserve to lose the game," said Neilson. "We had a man sent off, a shocking decision by the referee. I have got no idea what he was thinking about.
"He plays the ball and for some reason [the referee] gives him a second yellow card and puts himself in a really difficult position. He sends another guy off at the end similar to Tuesday night.
"If the referee referees it properly and doesn't give the second yellow then I think we go on and win the game."
Neilson spoke to referee Kevin Clancy in his room at full-time but was unimpressed with the response.
"You can't speak to the referee, it's a waste of time sometimes," Neilson added.
"He just said in his opinion it was a second yellow, but my opinion was it wasn't. People watching it on TV will see it but at the end of the day he makes the decision and we just have to get on with it."