Alan Archibald's side ended their home hoodoo in style on Saturday as they shocked the high-flying Dons 3-1 to record their maiden Firhill league win of the season and climb to 10th in the table.
The Jags now head to fellow-relegation battlers Ross County this weekend aiming to record back-to-back top-flight wins for the first time this term and move further away from the play-off spot that is now occupied by St Mirren.
There are just six fixtures left before the split and Balatoni is confident Thistle have what it takes to retain their Premiership status.
He said: "We've always believed that we can stay in this league and we still do.
"It was a huge result for us and it gives us a lift going into this week. We have already beaten them up there and hopefully we can do that again.
"I hope we can come back down the road happy and a bit further away from the play-off spot. It is probably going to go right down to the wire.
"Hopefully this win is the start of a bit of momentum for us and we can get a few wins under our belt before the split.
"That is when there are going to be a few huge games for every club near the play-off spot. Hopefully we can drag ourselves away from it."
Balatoni played his part at both ends of the field on Saturday, with the defender opening the scoring in the second half after Paul Gallacher had saved Barry Robson's penalty after just 16 minutes and putting in a solid shift alongside Lee Mair at the heart of the Jags rearguard.
A Lyle Taylor double either side of Adam Rooney's consolation strike won it for the Jags as the on-loan Sheffield United star took his tally to five following his January switch to Firhill.
Balatoni said: "He should have had five on Saturday, shouldn't he?
"I said when the manager brought in these players that it added a bit of freshness and quality. It brings the quality up in training and games and Lyle took his two goals well.
"He could have had four or five if he had had his shooting boots on. He scored two, so you can't give him too much stick!"
After finally ending their long wait for a league win on home soil, Thistle have given their Premiership survival bid a timely boost as they look to ensure their return to the top flight is not a one-season wonder.
And Balatoni has paid tribute to the Firhill faithful for their support as Archibald's side brought their barren run to an end.
He said: "The fans want us to stay in this league as much as we do. Nobody wants to go back down a division and nobody wants to finish in the play-offs. We are trying our hardest and their backing means a lot to us.
"They are still coming out in their numbers and they are making their voices heard to spur the players on. It is a big thank you to them."
Archibald admitted he could not celebrate until the end after his side lost two late goals in their 4-3 defeat at Motherwell the previous weekend.
He said: "We watched a DVD of the game to see what happened for us to lose that match, so I was actually waiting for the whistle from the referee after our goals, just to be sure how I should react.
"We showed great character in the second half after a first half when we appeared nervous and were not passing the ball well.
"We've got to go on from this and continue to show more belief and character and it's a big lift for us that we have also moved up a place in the table."