The Italians had looked like leaving London with the point they needed to secure their place in the knockout stages and dump Spurs out, but substitute Eriksen lashed home with 10 minutes remaining to move Mauricio Pochettino's side level on points with them.
Tottenham now travel to Group B leaders Barcelona – who have already qualified for the knockout stages – in two weeks' time knowing that a win would see them join Ernesto Valverde's side in the next round.
Spurs – who hit the crossbar through Harry Winks in the first half – had looked set for disappointment until Eriksen finished a fine team move involving Moussa Sissoko and Dele Alli to keep them firmly in the hunt for second place.
Harry Kane was denied by Samir Handanovic at his near post, while Alli fizzed over the crossbar from 20 yards as Tottenham started brightly.
Erik Lamela flashed wide from distance shortly before the halfway mark in the first half, while Lucas Moura fired straight at Handanovic after a swashbuckling run from Sissoko.
Pochettino's dominant side came agonisingly close to breaking the deadlock seven minutes before the interval, but Winks' curling effort from 25 yards crashed back off the crossbar.
Inter started to come out of their shell in the second period with Milan Skriniar prodding wide at the back post and Ivan Perisic denied by Hugo Lloris.
The visitors' backline looked set to hold firm, but Eriksen – who scored in September's 2-1 defeat to Luciano Spalletti's side at San Siro – had other ideas.
The Denmark international showed superb composure to thump past Handanovic from eight yards after being teed up by Alli to keep his side's Champions League adventure alive for at least another fortnight.
What does it mean? Spurs leave it late
One point from their opening three games looked to have ended Tottenham's hopes of reaching the knockout stages, but they have proved they are made of stern stuff under Pochettino with two wins on the spin putting qualification in their own hands. Inter will be kicking themselves for letting a point slip through their grasp and now need to better Spurs' result against Barca when they take on PSV.
Winks looks the part
The 22-year-old has not looked out of place on Europe's biggest stage this season and again proved why he is so highly rated by Tottenham with a composed display. He was only the width of a crossbar away from scoring a superb goal in the first half.
Lamela lucky to avoid red
The Argentina international endured a difficult game, too often making the wrong choice when in promising positions. He can also count himself very lucky not to have received his marching orders for an ugly tackle on Marcelo Brozovic.
Key Opta Facts
- Inter have never drawn in an away Champions League match against an English side (W3 L5).
- Inter have failed to score in three of their last four away games in Champions League.
- Tottenham and Inter are two of the seven sides yet to find the back of the net during the first 30 minutes of any game in the Champions League this season.
- Borja Valero made his 50th Inter appearance in all competitions.