The attacking midfielder opened the scoring with a sublime free-kick in the first half of the semi-final second-leg clash at Bramall Lane.
Che Adams, an 18 year-old signed from non-league Ilkeston Town, came on as a late substitute for the hosts and gave the gave the Premier League side a scare with a quickfire double that levelled the tie at 2-2.
However, Eriksen broke the hearts of the Yorkshire club by sliding in a cool finish two minutes from time to wrap up a 3-2 aggregate win.
And the Denmark international is eagerly awaiting a trip to Wembley where Tottenham will meet rivals Chelsea in a repeat of the 2008 final, which they won 2-1.
"I'm really happy and excited to play at Wembley, happy to score twice and delighted we're on our way to the final," Eriksen told the Tottenham official website.
"We started well, fought hard and got ourselves in a good position but they came back and put us under a lot of pressure.
"But we've showed that we can play under pressure and we did it again - it's not the first time we've scored in the last minute.
Eriksen has made a habit of proving the hero in the closing stages of matches, having scored late winners in Premier League victories against Hull City, Swansea City and Sunderland this season.
"I just wanted to get it on target and luckily it went in," he added.
"It was a really nice feeling. It's after you score that you get all the thoughts that we'll be at Wembley next."
