It also ended a winless run of seven games in all competitions which the German head coach suggested was 'ordinary' for a side continuing to punch above their weight in the top flight.
Have a look below at the full transcript from the post-match interview in which Wagner reflects on the historic win, inconsistency of results and Aaron Mooy.
On the 'extraordinary' win over Manchester United
This is one of the proudest moments for me as a manager since I arrived at Huddersfield Town and I know the supporters were desperate for this as well - it is one of the best moments in the history of this proud football club.
I was pleased to watch small Huddersfield Town beat Manchester United – a deserved victory from my point of view.
We changed the formation a little bit, we changed the game plan a little bit – we wanted to work more on the transition than ball possession.
And for 60 minutes it worked – Manchester United only had one shot on target and then in the last 30 minutes we then saw how strong they are.
We had a good goalkeeper today and some moments where we were lucky but I think the togetherness, the spirit and the attitude was extraordinary and why this extraordinary result was possible.
On showing true 'Terrier Spirit'
If you want to be competitive against Manchester United you have to be on your best in terms of the characteristics we have set at this football club.
It's great the lads have got the rewards out of what they have shown and it is a very happy dressing room at the moment.
On the inconsistency of recent results
It is easy to explain – what we have seen against Swansea City is usual for our football club and our players.
What we have seen today is the extraordinary and we should never take it as guaranteed – that would be a big mistake.
We have to accept performances like Swansea and West Ham United can happen, you shouldn't make it a big issue and only have to ensure you know what you have to do - you have to know exactly what is ordinary and what is extraordinary.
We are working day-in/day-out in the extraordinary and we have had more of them than ordinary but we have to not take it for granted.
Today was something very unusual – a huge win and moment for this football club. We've beaten Manchester United. Great stuff.
On Jose Mourinho reaction to the defeat
We only had a brief chat but as I said to the players before the game – I hope and believe we can get a result but I do not expect one.
All I expect is we show the right attitude, togetherness, spirit and if there is a chance to take then we have to go out and try to grab it.
We were on our best, Manchester United were perhaps not on their best and this is why the result was possible.
We have seen in football, everything is possible and we have seen other miracles in the past.
But today was less of a miracle and more showing the right attitude against a Manchester United side perhaps not at their best.
On the Premier League quality in the side
They have it but the competition has it as well so we can't take anything for granted – this result is something unusual and we have been working with the unusual day in/day out since I have arrived.
Hopefully we can produce some more performances like we have produced in the last two years as we are so ambitious and we will not give ourselves any limit.
But we are still aware of what is realistic and what is unrealistic and we cannot guarantee whatever happens in the future is positive but we will guarantee we will work on it.
We now have 12 points in the table, we have beaten Manchester United and everyone will get a lift and confidence out of this.
But we should not get too carried away – win, lose or draw leave what we have done in the past and be focused on the next one.
On Aaron Mooy as a 'Number 10'
He's not really played in that position against Manchester United - we really played with three number sixes instead and was more 4-3-3 or sometimes 4-1-4-1.
This was the right formation to play today but we will see what happens in other matches.