Hull led at half-time in Sunday's clash at the KC Stadium courtesy of Jake Livermore's early goal in his first appearance against the London club since leaving White Hart Lane.
The pivotal moment came five minutes after the break, when Gaston Ramirez was shown a straight red card for tangling with Jan Vertonghen off the ball.
Hull manager Steve Bruce was furious with that decision and Tottenham made the most of their numerical advantage as Harry Kane equalised just after the hour-mark with his 11th goal of the season.
Kane was on hand to turn the ball home after Eriksen's free-kick had struck the post and the Denmark midfielder secured all three points in the final minute, when his right-footed strike found the far corner of the net.
Tottenham have made a disappointing start to the season, but they are now up to 10th place and just two points behind fourth-placed Manchester United.
Arsenal and Liverpool were both beaten this weekend and Eriksen believes Tottenham can build on their win and challenge for a place in the top four.
He told Sky Sports: "In the first half we started slow then we were quicker. With the 10 men it helped us and gave us space.
"I'm going to sleep pretty well tonight. It's nice to see those teams expected to be in top four lose this weekend and us get the points. A few wins and we'll be up there again."
