Phil Jones inadvertently turned Kieran Trippier's cross into his own net in the 28th minute when the United defender was under no immediate pressure.
The visitors barely created any chances and only registered three shots on target, and new signing Alexis Sanchez was far off the pace playing his new side, as the former Arsenal winger was constantly hounded and booed by the Spurs home fans.
Defeat left United second in the table but a huge 15 points behind runaway leaders Manchester City, who beat bottom club West Bromwich Albion 3-0 at the Etihad Stadium.
Victory saw Spurs close to within two points of the top four and a Champions League place, and Eriksen told BT Sport: "It feels a bit weird to score from your first touch". "He arrived here aged 9-years-old and spent many years in the academy, he has been waiting for an opportunity which I give him now and again, today is another one".
"They have some of the best players in the country, a very good manager and are a very hard opponent". We knew everything. Then we don't press the ball, one mistake. "We are trying to finish second".
"And, at the moment, the fight is open for second, third, fourth, fifth and sixth but it is practically closed for the first".
They conceded a Christian Eriksen goal in a matter of seconds and never got a foothold in the game. "I don't think it's a big thing but he was telling us he couldn't carry on".
Mourinho has claimed he wants his side to be properly challenging for every trophy come 2020, and while there have been some good points this season, against the big sides they simply haven't been at the races - and to actually win proper trophies, that will have to change. He's a player that you miss on the pitch.
Tottenham manager Mauricio Pochettino, speaking after the match, praised his players for putting up a fantastic performance.
Fellaini is unlikely to feature in United's next game now, a Premier League clash at home with Huddersfield Town, as the reoccurrence of his injury is expected to keep him out of action for a few weeks at least.
Another said: "Interesting tactic of dropping our best outfield players".