The striker equalised after Albert Adomah's smart opener, before Ipswich cruised to a deserved three points with an accomplished second-half performance.
Luke Chambers headed in a deep Aaron Cresswell cross after 57 minutes before McGoldrick burst clear of Jonathan Woodgate to slot home in injury time.
McCarthy, who remains second favourite, behind Martin O'Neill, for the vacant Republic of Ireland job, said: "I thought McGoldrick was outstanding and he has been all season.
"He has not been getting the goals, but the keepers have been making unbelievable saves.
"He puts in a real shift and he is a proper player. We are lucky to have him."
McCarthy's training ground message before the visit of Middlesbrough was to urge his players to break into the box, and it worked a treat as right-back Chambers popped up to give Ipswich the lead.
The Ipswich boss said: "It is a bit alien for Luke as he normally plays centre-half. But I encouraged all of them in training to take a chance in the box. Chambo got a goal by taking that chance.
"Middlesbrough were better than us for the first 20 minutes, but I thought after that we deserved the three points.
"I want all my players to put in seven-out-of-10s week-in, week-out, and today they worked very hard."
While McGoldrick shone for Ipswich, Middlesbrough boss Mowbray was left to reflect on a poor start to the season that has yielded just one win from six games.
It could have been even worse for the visitors after goalkeeper Jason Steele made a string of fine saves and young Ipswich midfielder Luke Hyam missed a golden chance with the goal at his mercy.
Mowbray said: "They deserved the victory for the honest and hard work they put in.
"For 20 minutes, we played some pretty decent football and got ourselves deservedly in front.
"But Ipswich are a team who do the basics well. They close you down, put their foot through the ball in defence and ask questions of you, and we fell a bit short defensively.
"We need to learn lessons and find a way to play against teams who work so hard to press the ball. We didn't ask enough questions of Ipswich in the second half."
Mowbray said: "In the last quarter of an hour, we pushed both full-backs forward and left ourselves one-on-one. That means you are going to be vulnerable."