The West Lothian outfit were at Cavalry Park to take on Portobello in the first round and they came away with a 38-7 victory.
As well as Plenderleith, Stuart Bell, Stuart Cunningham and Mark Green all went over for tries for the visitors with Chris Ronaldson kicking the remainder of the points.
Linlithgow director of rugby Gordon Dixon said: “The guys put in a really good first-half performance to give themselves a good lead and although they took their foot off the gas a bit in the second half it was a good afternoon’s work. Portobello also contributed to a good match.”
Other winners in round one on Saturday were Edinburgh University Blues, Musselburgh and Forrester.
The students saw off RHC Cougars 25-15, Musselburgh thumped Ross High 81-12 and Forrester edged out Lismore 24-20. Preston Lodge had a walkover against North Berwick.
Forrester will take on Edinburgh University Blues in the last eight, Livingston will play Musselburgh, Murrayfield Wanderers will face Linlithgow and Preston Lodge will travel to Trinity Accies – all on December 10.