The Team Dimension Data rider, 33, timed his push perfectly on the final climbs of the 194.5km stage from Bradford to Fox Valley near Sheffield.
Pauwels' team-mate Omar Fraile finished second and Britain's Tao Geoghegan-Hart, riding for Team Sky, was fifth.
Nacer Bouhanni, Saturday's stage winner, was taken to hospital after being knocked unconscious in a crash.
Pauwels attacked at the top of the Cote de Wigtwizzle, with 22km remaining, then eked out a 30-second lead on the Cote de Ewden Height.
The chasing pack narrowed that advantage to nine seconds by the summit of the final climb out of Midhopestones but Pauwels eased clear again to claim victory.
"It feels a bit strange," Pauwels said. "It is the first time I have had my hands in the air.
"But I think people would not really be surprised that I take a win because I have been quite close.
"Last year I was second, third, fourth, everything except a win, and now I get two wins at the same time which makes it more special."
Men's Tour de Yorkshire, stage three result:
1. Serge Pauwels (Bel/Team Dimension Data) 4hrs 57mins 47secs
2. Omar Fraile (Spa/Team Dimension Data) Same time
3. Jonathan Hivert (Fra/Direct Energie) +6secs
4. Brent Bookwalter (US/BMC) Same time
5. Tao Geoghegan Hart (GB/Team Sky) +8secs
Men's Tour de Yorkshire, final classification:
1. Serge Pauwels (Bel/Team Dimension Data) 11 hrs 53mins 4secs
2. Omar Fraile (Spa/Team Dimension Data) +6secs
3. Jonathan Hivert (Fra/Direct Energie) +7secs
4. Brent Bookwalter (US/BMC) +18secs
5. Matthew Holmes (GB/Madison Genesis )+20secs
Belgian Serge Pauwels claimed his first career win in the Tour de Yorkshire after winning Sunday's final stage.