Thistle returned to the top flight in a high-tempo goalless encounter against United and have lost just twice this season ahead of their League Cup third-round clash at Tannadice.
"They have been really good," Dillon said. "They gave us a really good game on the first day of the season and it's no real surprise that they have continued that.
"You get people who say 'they won't last' or 'they will die off a little bit after the early few games'. But I didn't agree with that at the time and I still don't.
"They are a really good side and have really good players and we know it's going to be a tough game.
"They were very well organised and they pass the ball out from the back. They work really, really hard as a team and look after each other. That showed when we played them."
Thistle boss Alan Archibald has been delighted with his side's start to the campaign after two away wins and three draws at home have taken them to seventh place in the Scottish Premiership.
The Firhill outfit were among many people's list of favourites to go down but their early season form has been impressive.
Now the Maryhill manager wants to see the same verve injected into their cup hopes.
He said: "We have possibly proved a few of the people who doubted us at the start of the season wrong but we are only seven games into the season.
"There is still a long way to go but we are delighted with the way we have started. I'd have preferred if we had picked up a few more points but it's been good so far.
"Now we can turn our focus to the League Cup and it's very much a priority for us because our record in this competition over the last five years has been poor. It's a chance to get to a quarter-final for us and that's a big deal.
"I played in the Scottish Cup semi-final against Rangers back in 2002 and it was a fantastic occasion.
"We said that to the players even last year when we got to the Ramsdens Cup final. It's not often that you get experience these kind of games, so you cannot take it lightly when the chance comes along."