The Omega Pharma-QuickStep rider rode clear of the bunch as Swift paid the price for making his move too soon.
"It was a great stage, a great victory, my first for the year with Omega Pharma-QuickStep," Renshaw told reporters.
"It's always good to win, I've had victories here before on the Tour of Britain and it's good to do it again."
Renshaw, 31, takes the yellow jersey from Marcel Kittel, who lost touch with the peloton on the Great Orme.
Stage three of the Tour of Britain, from Newtown to The Tumble, Abergavenny, takes place tomorrow.