Patterson stroked the ball into the bottom corner in the 26th minute and then fired home a penalty five minutes into added time in the second half.
The goals brought Patterson's overall tally for the season to 20.
Derry finished the campaign with four wins and had already qualified for the Europa League by finishing third.
Shaun Patton was handed a start by Derry manager Kenny Shiels after regular goalkeeper Ger Doherty had played every minute of every previous game for the Candystripes this season.
Patton saved from Steven Kinsella early on but Patterson made no mistake at the other end by sidefooting in the opener.
The striker was almost on target again soon after when he hit the bar and Rory Holden steered his first-time shot with the goal gaping.
Patterson did grab his second with his last-gasp spot-kick after he was brought down by Rory Feely, who received a red card.
Derry City ended their season on a high as Rory Patterson scored both goals in a 2-0 Premier Division win over St Patrick's Athletic at Richmond Park.