Despite the history they were making, Ararat-Armenia did not seem overawed by the occasion early on and almost took the lead inside 30 seconds.
Artur Serobyan’s delivery was waiting to be tapped in at the far post by Sandro Lima but, with the goal at his mercy, the ball instead rolled under his foot and the chance went begging.
The hosts were riding the wave of momentum in the early stages, going close to breaking the deadlock on two more occasions in the opening 10 minutes.
First, Edgar Grigoryan fired straight at Jakub Surovcik from close range, before Lima headed Hugo Oliveira’s delivery against the woodwork.
There was always a possibility that Ararat would be left to rue their missed opportunities, and that proved to be the case when Sparta hit them with a quick-fire double.
The goals came from an unexpected source, as centre-back Tobias Guddal first flicked home Adam Karabec's corner before reacting quickest to a loose ball on the edge of the area to guide a sumptuous effort into the top corner.
In response, Araret rarely threatened to get back into the game besides defender Jose Junior Julio Bueno's solo attempt, as he bombed forward down the right and flashed a ferocious effort narrowly wide of the target.
The destination of the third goal felt crucial in deciding who would prevail, and it ultimately went the way of the Czech side within 10 minutes of the restart.
After driving towards the byline, Josimar Alcocer fizzed a ball across the face of goal for John Mercado to tap home and put Sparta in total control.
Nevertheless, Ararat were not prepared to go down without a fight and reduced the arrears to two almost instantly, when Bruno Wilson headed home from six yards.
However, any visiting fears of a comeback were extinguished 18 minutes from time, as Matej Jurasek’s marauding run down the right culminated in him standing up a perfect delivery for Patrik Vydra to head home.
From there, Sparta cruised to victory, ending a mini-run of two consecutive away defeats in European competition.
In contrast, Ararat’s evening didn’t go to plan and, with all their home UEL games this term being played on neutral turf, their quest to secure an unlikely progression looks difficult.
Flashscore Man of the Match: Tobias Guddal (Sparta Prague)