Spurs continued their bright start under new head coach Tim Sherwood, making it three wins from the four Premier League matches he has taken charge of.
|11/1||Tottenham are 11/1 with William Hill to beat Arsenal 2-1|
The champions produced an immediate response through Danny Welbeck but were unable to find an equaliser despite enjoying strong spells of late pressure, much to the delight of Spurs' Danish playmaker.
"I couldn't have wished for a better start to the New Year than a goal and assist in a win at Old Trafford," Eriksen said.
"I'm really happy with the win and if you score, it's an even better feeling. We got to 2-0, they came back quickly and we had to keep going."
The result continued United's recent home woes, with David Moyes' men now having lost three of their last four league fixtures at Old Trafford.