0750 GMT October 18, 2018
The Spaniard made 14 saves, equaling the record since statisticians Opta began collecting data.
"You need the keeper to be there for you when the team needs," added Mourinho.
Arsenal boss Arsene Wenger said De Gea was "absolutely outstanding".
Wenger's side fired 33 shots at goal, with 15 finding the target. The United resistance prompted the Frenchman to state De Gea was "man of the match by a clear mile".
Only Tim Krul – for Newcastle against Tottenham in 2013 – and Vito Mannone – for Sunderland at Chelsea in 2014 – have recorded 14 saves in a game since Opta began gathering this piece of data in 2003-04.
Most remarkable of all was a double De Gea save to deny Alexandre Lacazette and Alexis Sanchez with the score at 2-1 early in the second half.
De Gea played down his role, saying it was simply a "good game for me" before focusing on the "confidence" United can take into this week's Manchester derby at Old Trafford. Mourinho added, "I told De Gea after the match, what I saw today was the best from a goalkeeper in the world.
"I loved the way my team played and fought. Arsenal played in some period amazing attacking football – creating difficulties for us.
"But I have to say that my players deserve all the great words. I don't know so many in English but amazing, phenomenal, fantastic. They deserved three points."
"Despite being 2-0 down we should have come back – we had enough chances," said Wenger, whose side are now fifth.
"It was a big blow to go 2-0 so early on – especially at home. We were too on the edge mentally maybe – you cannot be in a game like that.
"We played well but there is nothing more frustrating when you have that quality of performance and nothing to show for it at the end. The attitude was impeccable until the end. But you cannot make the mistakes we made at the beginning."
Mou opens up
Mourinho has garnered a reputation for defensive setups on trips to the league's traditional big clubs but his side went after its host early on, hounding possession high up the pitch to great effect.
United’s opening two goals owed much to slack use of possession by the home side but needed clinical finishes, notably when Martial cleverly flicked into the path of Lingard for the second.
The reward for United’s adventure secured a first win for Mourinho in his past 12 away fixtures against the 'big six'.
Wenger labelled De Gea "absolutely outstanding" but while his brilliance points to United riding its luck at times, the Red Devils were impressive in offering a balance between defense and attack.
Nemanja Matic was consistently well placed, never more so than when blocking a goal-bound Aaron Ramsey shot with the score at 2-0.
And the presence of the defensive midfielder once again freed Pogba, who in bursting into the box to lay on Lingard's second now has five assists this season, surpassing his four in the previous campaign.
Whether Mourinho will choose to live so dangerously against Manchester City this week remains to be seen, but those watching from a neutral stance would be fortunate to see a game as good as this one again.