The League of Ireland Premier Division side went ahead early on through Michael Duffy and Barry McNamee (14) doubled their advantage.
Northern Ireland forward Patterson scored his first on the hour mark and then netted twice (84 and 86) - the final goal of the game being a penalty - to complete the rout and set up a tie with FC Shakhtyor Soligorsk of Belarus.
Two other League of Ireland Premier Division outfits Sligo Rovers and Dundalk also progressed to set up a clash with Norwegian side Rosenborg.
Sligo beat Lithuanians Banga, with whom they had drawn 0-0 away, 4-0 at the Showgrounds.
Alan Keane put the hosts 1-0 up in first-half stoppage time, and after Karolis Urbaitis was sent off for the away side in the 68th minute, Sligo made the most as Aaron Greene (72), Danny North (83) and David Cawley (89) also got on the scoresheet.
Dundalk saw off Luxembourg's Jeunesse Esch 3-1 at home for a 5-1 aggregate victory, with goals from Brian Gartland, Kurtis Byrne and John Mountney.
Motherwell, the Scottish Premiership runners-up, enter the competition next week when they will face Icelandic outfit Stjarnan at Fir Park.
Stjarnan were making their Europa League debut this week but carried too much firepower for Bangor City, wrapping up an 8-0 aggregate win with a 4-0 success in Wales on Thursday.
Airbus UK Broughton bowed out of the Europa League after a 2-1 defeat to FK Haugesund in Norway.
Torbjorn Agdestein scored from close range to give the hosts the lead but the Welsh side were level when Mike Pearson fired home from 12 yards.
Maic Sema scored Haugesund's winner before Airbus's Jordan Barrow was sent off for a second yellow card.
Paul Heatley scored twice as Crusaders beat FK Ekranas 2-1 in the second leg of their Europa League qualifier in Lithuania, winning 5-2 on aggregate; the IDanske Bank Premiership side will face Swedish club IF Brommapojkarna in the next round.
Glenavon lost 3-2 at home against FH Hafnarfjordur of Iceland, going down 6-2 overall.