The two-time Lowland League champions required an additional 30 minutes to see off their East of Scotland First Division Conference X opponents 4-3 at Ainslie Park to progress to the last 16 of the competition.
However, key duo Jamie Dishington and Michael Herd were both forced off through injury as Samuel admitted the club's injury list is getting longer by the week.
Dishington was on target for Spartans who actually fell behind to the Grangemouth-based club inside the opening 10 seconds.
Samuel said: "With three players making their debuts, it was a day to remember for some, but sadly we lost Herdy and Dishington during the game to injury to add to an already lengthy unavailable list. We're delighted to get through. It's cup football and it's all about progressing to the next round. I have to give Syngenta a huge amount of credit for being so positive, for committing numerous players forward throughout the game. I'm sure they will kick on and lift the East of Scotland Conference X title if they compete week, week out as they did against us.
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"For our part we continue to create lots of chances and scored some good goals."
Elsewhere, Linlithgow Rose are also safely through after clocking up an incredible 20th straight win under boss Gordon Herd as they overcame West of Scotland Premier Division outfit Blantyre Vics 2-1 at Prestonfield.
Goals from Sean Heaver and Gary Thom sealed the win despite a late strike from the visitors' Sam MacKenzie.
Herd said: "It would be a huge cup to win and as a management team and as a squad we want to be pushing to be in the mix. A club like Linlithgow are expected to challenge for big honours."
Meanwhile, Broxburn registered a 3-1 win over Tynecastle in East of Scotland League Premier Division's game of the day, but bottom club Whitehill Welfare were beaten 3-2 on their home patch by Hill of Beath. The Ferguson Park side remain seven points from safety following their latest setback.