It was a sweet first-time shot as Lee Miller played a ball into him after a run through the middle had stretched Colchester's defence.
It was Goodfellow's third goal in four matches since his £100,000 move from Stoke City and it lifted his new club to within two points of second-placed QPR.
His manager Danny Wilson said: "We have now closed the gap on the two sides above us and that is what matters.
"This wasn't a classic but defensively we did well and young Marc is going to get better as he goes along."
Goodfellow's latest goal made up for an astonishing 13th minute miss from a corner. The ball fell to him after Lee Peacock's sharp header had been parried by Richard McKinney in Colchester's goal.
But from three yards, the youngster somehow lifted his shot over the bar.
"Don't ask me how I did it. I just don't know," he confessed. "That's what made my goal so much sweeter - a great start, another game and another goal."
Colchester failed to match the drive that the Robins had from their midfield captain Tom Doherty and managed only one direct shot on goal.
That was a long-range effort late on from Thomas Pinault but keeper Steve Phillips had it well covered.
Colchester boss Phil Parkinson has a growing problem though with Craig Fagan, the loanee from Birmingham.
He was sent off for a double booking, a foul on Phillips in the first half and then talking back to referee Frazer Stretton.
He has now been dismissed twice this season and collected 11 yellows.
His manager said: "I haven't spoken to him about it but I've just got to sit down and think what I can do with him."