Aitor Karanka's team took the lead at Portman Road through Christian Stuani before Nugent scored his 15th goal in 14 career matches against Ipswich to seal the points.
Middlesbrough are now one point clear of second placed Brighton, who can regain top spot if they beat Charlton on Saturday.
The visitors broke the deadlock in the 54th minute when Albert Adomah found space for a dangerous cross that was headed in at the back post by Stuani.
Nugent, who joined Middlesbrough earlier this year after a four-year spell with Leicester, wrapped up the win in the 74th minute.
Stewart Downing's incisive pass found Nugent but he still had a lot to do, with his low shot taking a slight deflection off Tommy Smith before finding the net via the inside of the post.