The Welshman was part of the Team Sky unit that had been attempting to help world champion Mark Cavendish claim the victory.
However, with around 1km of the race between Ipswich and the Norfolk County Showground remaining, Cavendish was involved in a collision that left him with a suspected shoulder injury.
Rowe took advantage of Cavendish's misfortune to take the stage in a time of 4:51:06.
"Cav was behind and it was all set up for him," Rowe told reporters at a press conference attended by Sports Mole. "When he went down I looked back and shouted to Brad (Wiggins) that it's for me now.
"I went full gas and managed to out-fox the guy that was next to me and in the end we managed to win it. It's turned out pretty perfect."
The 22-year-old signed a two-year deal with Team Sky at the turn of the year.