The 24-year-old dominated the fight from start to finish at the Wembley Arena, fighting on the under card of Anthony Joshua's world heavyweight title defence.
The three judges were in no doubt who shone as they awarded the fight to Conway 100-90, 100-89, 100-89.
McGowan was a late substitute for Conway's original opponent, the French Olympic bronze medal winner Souleymane Cissokho.
With the bout being broadcast live across the world on Sky Sports Box Office and DAZN, Conway took his chance to show what he is capable of, dropping his opponent om his way to an emphatic victory.
And the Northampton fighter, who trains out of the Team Shoe-Box gym in Duston, immediately set his sights on targeting a re-match with Ted Cheeseman, with the pair having drawn in their previous bout for the British title in the summer of 2019..
“I’m coming for Ted Cheeseman, there’s no hiding," said Conway.
"I’ve been wanting the rematch since the fight first happened. We’re both a similar age and we’ll both want to put it behind us so that we can move on.
“McGowan was really tough and came in at late notice. He gave it is all but I did what I had to do. I want to be as active as possible from now on.
“Super-welterweight is where I want to campaign at for my titles. I want to defend my title at super-welterweight and then win the British title at this weight too.”