The Candy Stripes came away with a 5-0 win over Aberystwyth Town to seal the tie 9-0 on aggregate.
Michael Duffy and Barry McNamee gave City a 2-0 lead at the break.
Patterson scored his first on the hour mark before adding to his tally in the 84th minute.
A penalty four minutes from time secured the match ball for the player.
Derry face FC Shakhtyor Soligorsk of Belarus in the next stage of the competition.