After 1–1 at full time and extra time, Nottingham could win the penalty shootout with 5–4.
Thus, the season's surprise team, third in Premier League, will face Brighton away in the quarterfinal.
Jens Cajuste scored one of the penalties for Ipswich, while Elanga was substituted in extra time and therefore was not an option as a penalty taker.
The first nine penalties were scored before Ipswich's Jack Taylor missed the tenth and final one.
Ipswich, in the relegation zone in Premier League, took the lead in the 53rd minute when George Hirst headed in 1–0 after a corner.
But the lead only lasted for a quarter of an hour.
Ryan Yates headed in 1–1 in the 68th minute on Anthony Elanga's perfect pass.
The quarterfinals in the FA Cup will be played on the weekend of 29–30 March.
