The South African seamer sent back Tom Banton, Roelof van der Merwe and Lewis Goldsworthy with the first, second and fifth balls of the 49th over to send the hosts crashing towards 181 all out in their second innings.
Paterson finished with figures of four for 46 in a victory by an innings and 160 runs, completed in the final session of the third day.
Notts skipper Steven Mullaney said: "It's the first time I have won a four-day game here and I have been playing for quite a while, so we are delighted.
"It was a bowl first pitch and I think Somerset will be disappointed with the lengths they bowled, but credit to our batsmen for getting stuck in.
"To score 448 on that pitch in overcast conditions was an outstanding effort.
"We were relentless with the ball after that and even when we weren't taking wickets, we were not going for runs.
"If we keep playing like that, we will put sides under pressure in our remaining games. We still have three very good teams to play, but we will focus on ourselves. I believe in the squad and the support staff and that we are building something special."
Nottinghamshire took 23 points to their opponents’ two to overtake them in the Division One table.
Somerset had started the day on 87 for seven and trailing by 361.