The 'Red Devils' were in front inside three minutes, having won a penalty after 75 seconds, and they looked nothing like the side that limped home last season.
The wing backs were pressing forward, the midfielders worked well in tandem, and Leicester were unable to cope with the home side's fluid play at first.
"It was definitely a positive night for United, who picked up three points against difficult opponents - and there is lots more to come from them," Dublin said.
"United were outstanding in the early stages and I think the Foxes were in shock at the way they came out of the blocks and took control of the game.
"It was almost as if they were saying 'look this is Old Trafford, and we are United - this is how we play'.
"Their first thought when they got the ball was always to get it forward and they were trying to get their wide players high up the pitch, which is the United way.
"It was very exciting to watch for the first 20 or 25 minutes but, when they took their foot off the gas, Leicester came right back into the game."
The hosts eventually ran out 2-1 winners, but it was an uncomfortable ending as Jamie Vardy netted a late goal, before Kasper Schmeichel almost equalised.