Craig Brewster insists the Dundee United players must believe they can avoid relegation if they are to do so.
The former Dundee United striker and boss credits manager Mixu Paatelainen for giving the Premiership's bottom team hope.
"Mixu has got a team together that believe they can win and that's crucial," said Brewster, assistant to Derek Adams at Plymouth Argyle.
"Suddenly they have put Kilmarnock under real pressure."
United are five points behind Lee Clark's Killie with one game remaining until the league splits into a top six and bottom six.
Thereafter both teams will have five games to avoid being relegated automatically or playing either Falkirk, Hibernian or Raith Rovers from the Championship in the Premiership play-off final.
In recent weeks the Terrors have drawn 2-2 with Dundee and enjoyed a 1-0 win over St Johnstone but they lost on Tuesday to Partick Thistle despite dominating the first half.
"If they can keep bringing Kilmarnock closer and closer then they've got to believe they can do it," Brewster, 49, told BBC Radio Scotland.
"It's not looking good but they have rallied very much of late.
"It was a disappointing result the other night, but Mixu has got points and they have given themselves a real lifeline.
"I think they've got it in their grasp. They were that far out of it everybody just expected United to go down so they had nothing to lose.
"As long as they are playing well and having the belief that they can overcome it, that's the major part."
Brewster, who played for United from 1993-96 and again in 2006 when he was also the manager, said the remaining match between United and Kilmarnock will be "massive".
"No-one wants to go down but having done so well over the last few years it is a big disappointment this year to find themselves down there," he added.
"I think the chairman has already said that they would have to cut major costs off their wage bill if they do go down.
"Nobody wants to see that so they've got from now until the end of the season to make sure that doesn't happen."