The Lilywhites made it back-to-back victories in Group B thanks to Eriksen's close-range finish 10 minutes from time, taking them level on points with their opponents with one game to play.
Tottenham, who hit the crossbar through Harry Winks prior to their deserved breakthrough, must now match Inter's result against PSV Eindhoven when they travel to Barcelona in two weeks' time.
Heading into the match on the back of a five-game winning run in all competitions, Tottenham had some wind in their sails as they went in search of an early breakthrough.
A Dele Alli shot over the bar aside, however, they struggled to really create any clear-cut opportunities in the opening half-hour.
One of four changes to the side that started the 3-1 win over Chelsea here on Saturday, Lucas Moura sent a weak shot down the middle for Samir Handanovic to keep out 33 minutes in following some good play from Moussa Sissoko in the build-up.
The closest Spurs came to a first-half opener was shortly after when Winks, another of those to return to the fold tonight with Sunday's trip to Arsenal in mind, curled the ball against the crossbar from just outside the box.
Spurs also had a penalty appeal rejected when Lucas was tackled right on the edge of the area by Matteo Politano, but they were perhaps fortunate to remain with 11 men on the field as Erik Lamela got away with a nasty two-footed stamp on Marcelo Brozovic late in the first half.
Inter, whose win at PSV Eindhoven last time out on their travels was their first in nine European attempts away from home, were more concerned about defending than attacking in the final 30 minutes.
The Italian side, winners of this competition in 2010, looked threatening on the counter and from set-piece plays, but it was Spurs who looked the more likely to net.
Group B has seen plenty of late drama this season, though, and with Eriksen and Son Heung-min both being brought off the bench for the final quarter of the game, Spurs got the goal that they badly craved.
Soon after Borja Valero had been kept out by a strong Hugo Lloris hand, Sissoko drove into the opposition box and laid the ball off for Alli, who in turn teed up Eriksen alongside him to lift it over Handanovic.
Despite suffering just a third loss in 14 matches in all competitions, Luciano Spalletti's men are still favourites to join Barcelona in the last 16 as they host PSV on the night that Tottenham travel to Camp Nou.
TOTTENHAM HOTSPUR (4-2-3-1): Lloris; Aurier, Alderweireld, Vertonghen, Davies; Winks (Dier 87'), Sissoko; Lamela (Eriksen 70'), Dele, Lucas (Son 62'); Kane
INTER MILAN (4-2-3-1): Handanovic; D'Ambrosio, Skriniar, De Vrij (Miranda 82'), Asamoah; Brozovic, Vecino; Politano (Keita 83'), Nainggolan (Valero 44'), Perisic; Icardi