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Bottom side United's first win in Perth in four years, and Kilmarnock's draw away to Partick Thistle, means the gap between them is down to five points.
"It was a wonderful effort. With 10 men, that spirit and character was there again," said the Finn.
"I can't praise the boys enough. They've got real mental toughness."
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Ryan Dow had put United into a deserved lead midway through the first half.
However, Saints came back into the match and when Coll Donaldson was sent off for denying Chris Kane an obvious goal-scoring opportunity, the visiting fans may have feared another damaging day in their bid to avoid automatic relegation.
St Johnstone midfielder Murray Davidson hit the crossbar as the home side pressed for an equaliser but United held firm.
"We still have a long way to go but that was a small step towards it," continued Paatelainen.
"The mood is positive. Killie will pick up points so we need to be strong. They have a quality manager, they have fantastic players in every department, but days like this will help our chances of survival and that's what we hang on to.
"I'm really pleased with everybody's effort."
Saints manager Tommy Wright was frustrated at his team's lack of bite in the first quarter of the match.
"Up until they scored we didn't compete well enough, didn't make enough tackles, didn't win enough first headers or second headers," he lamented.
"I thought we got a slap in the face with the goal and we were much better after that. Probably they've defended well enough overall to win the game.
"When you give a team something to hold on to, even with 10 men, it makes it really difficult."
Alan Mannus had made two impressive saves prior to the United goal but he will have been disappointed to have allowed Dow's shot past him.
"I think in the build-up to the goal we should have done better," said Wright.
"We dropped too deep and we should have dealt with the cross better. He got a free contact inside the box.
"Because Alan was on the move, it hit the underside of his body and squirmed over the line."

"This is definitely not the Oscars," said 22 Jump Street star Jillian Bell on the red carpet in Los Angeles.
As well as fan-voted awards like best kiss and best shirtless performance (Efron won it - again) the ceremony was also an unofficial promotional platform for this summer's blockbusters.
The night's big winner was The Fault in Our Stars, which won best movie.
The film's star Shailene Woodley also picked up best female performance, the Trailblazer Award and best kiss for a scene with Ansel Elgort.
Woodley gave an emotional speech dedicated to John Green, the author of the book which the film is based on, saying "he gave this world a beautiful masterpiece".
Other winners included Bradley Cooper, who won best male performance for his role as the late Chris Kyle in American Sniper.
The 40-year-old actor said: "Chris Kyle would have turned 41 four days ago. Chris, this is for you," said Cooper.
Channing Tatum took home best comedic performance for 22 Jump Street and Meryl Streep picked up best villain for her role in Into the Woods.
Jennifer Lopez, Jennifer Lawrence, Seth Rogen and Rose Byrne were also among the winners.
Kevin Hart, who was the target of many size-related jokes throughout the night, brought his kids on stage to accept the comedic genius award.
He said: "I do it all for them. I'm trying to leave a legacy behind."
In one of the more energetic moments of the show, Robert Downey Jr brought his fellow Avengers stars to their knees while accepting the Generation Award.
Scarlett Johansson, Chris Evans, Chris Hemsworth, Mark Ruffalo and Jeremy Renner all took the stage to present their co-star with the award, which Downey called "the recognition I so desire".
Clips from the upcoming Pitch Perfect sequel, Judd Apatow's latest comedy Trainwreck and Marvel's new film Ultron were shown during a look ahead to this summer's releases.
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Mixu Paatelainen praised his Dundee United players' resolve as they beat St Johnstone 1-0, despite being reduced to 10 men for the last 30 minutes.
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Vin Diesel sang, Channing Tatum danced and Zac Efron showed off his abs, yes - again, at the 2015 MTV Movie Awards.