Robert Lewandowski’s early penalty had given Barca the perfect start at Old Trafford.
But the La Liga leaders were again undone on the European stage as Fred levelled early in the second period before Antony delivered his biggest moment since arriving in Manchester from Ajax.
“Magnificent night,” said Ten Hag, who has transformed United’s fortunes in his first season in charge.
“That is another step because when you can beat Barcelona, your belief can be really strong because you are then able to beat anyone.”
The fact that two of the continent’s giants were clashing at this stage of Europe’s second tier competition was evidence that both have fallen on harder times in recent years.
But United are riding the crest of a wave as they remain in the hunt for trophies on four fronts.
The Red Devils could end a six-year wait for silverware when they face Newcastle in the League Cup final on Sunday.
But they left nothing in reserve to secure their biggest European scalp since dumping Paris Saint-Germain out of the Champions League last 16 in dramatic fashion in 2019.
“I think we have some great personalities in this team,” added Ten Hag.
“Everyone has such a strong belief in this team, you can see it. With the subs they bring energy and quality, they bring a different dynamic in games.”
United are now unbeaten at Old Trafford in 18 games dating back to September but were forced to come from behind for the second time in the tie.
‘Different’ Barca failure
Barcelona were unbeaten in all competitions stretching back to October, when they were dumped out of the Champions League group stage at the hands of Bayern Munich and Inter Milan.
Despite their rise domestically under Xavi Hernandez to usurp Real Madrid at the top of La Liga, the Catalans again came unstuck in a big European test.
Barcelona also crashed out at the Champions League group stages last season before losing to Eintracht Frankfurt in the Europa League.
“My feelings were really different from last season,” said Xavi. “This year we have competed in every game apart from Bayern at home.
“For small details we haven’t won. We have to learn from our mistakes and improve.”
The visitors even failed to take advantage of a gift with the opening goal.
Bruno Fernandes foolishly stretched out an arm to catch Alejandro Balde and French referee Clement Turpin infuriated Old Trafford by pointing to the spot.
David De Gea got a hand to Lewandowski’s penalty, but the ball rebounded in off the post on 18 minutes.
Ten Hag responded by replacing the ineffectual Wout Weghorst with Antony at half-time and got the desired response within two minutes.
Fernandes, restored to his preferred central midfield role, picked out Fred, who fired low past Marc-Andre ter Stegen.
United still needed a big moment by De Gea to prevent the momentum from swinging back towards the Catalan giants as he tipped over Jules Kounde’s header from point-blank range.
Antony has flattered to deceive since being reunited with Ten Hag after an £86 million ($104 million) move from Ajax.
However, the Brazilian delivered a moment of quality befitting of that price tag for the winner 17 minutes from time.
After Alejandro Garnacho and Fred saw efforts blocked, the ball sat up nicely for Antony to curl the ball beyond the outstretched arm of Ter Stegen.
AFP