Sagan, a Slovak who rides with Cannondale, completed the 146-kilometer (91-mile) stage from Fanja to Al Bustan village in the heart of old Muscat in 3 hours, 48 minutes, 36 seconds. He finished 5 seconds ahead of RadioShack rider Tony Gallopin and IAM rival Martin Elmiger.
Sagan now leads Gallopin by nine seconds in the overall classification.
After catching up to an early breakaway, a pack of 50 riders reached the final sprint together, with Sagan proving strongest at the end.
"I'm really happy about this first win because the team wanted it and waited for it," Sagan said. "The fact that I took this win doesn't count for very much — what is important is that Cannondale Pro Cycling won. Having broken the ice means a run without pressure. We'll continue to work to achieve new successes at races throughout the year."
Wiggins, who struggled on the first day after being delayed by a crash, finished 11 seconds behind on Tuesday and is 1:42 behind Sagan. His teammate and Tour de France runner-up Christopher Froome finished seven seconds back, which leaves the Briton in sixth overall and 17 seconds behind Sagan.
"It was a good day for us and I'm happy with how we performed," Sky sports director Nicolas Portal said on the team's website. "It was very hard in those last 25 kilometers, especially with those two categorized climbs. The first one was very steep with a constantly changing gradient, but we had the numbers at the front and Pete (Kennaugh), Vasil (Kiryienka), Richie (Porte) and Bradley were able to control things right up until the second climb for Froomey."
Alberto Contador, who was stripped of a third Tour de France title for using a banned substance, finished 11 seconds behind Sagan and is 21 seconds back in 24th.