The Southampton loanee restored parity with the first professional goal of his career after Kayden Jackson’s opener.
Ivorian Francois Zoko turned the game on its head from close range and Olomola lobbed Aaron Chapman for his second and Town’s third of the afternoon.
Jackson pulled one back on 53 minutes but Yeovil held on to secure their first points of the term.
Manager Darren Way made two changes to the side that started against Wolves in the Carabao Cup at Molineux in midweek.
Bevis Mugabi returned from an ankle injury to take the right-back slot, while Southampton loanee Olomola partnered Francois Zoko up front.
Defensive duo Tom James and Daniel Alfei dropped to the bench.
Ranked in a 4-4-2 diamond formation, Yeovil began in positive fashion with Olomola looking to utilise his pace to stretch the visiting defence.
Otis Khan tested his aim early on, warming the gloves of Chapman from 25 yards before the Town wide man flicked neatly into Olomola’s path only for his teasing cross to flash across the face of the goal.
But the hosts’ dominance in the opening exchanges went unrewarded and Accrington took the lead against the run of play.
When Kee’s stinging strike was beaten back into play by Krysiak, Jackson was on hand to offer a simple finish leaving Yeovil’s backline searching for the linesman’s flag in desperation.
A quiet spell in the half ensued and then Olomola sparked the game back into life.
The young forward collected a loose ball in the area and rifled a brilliant left-footed shot into the top corner.
One almost became two from the restart.
Ryan Dickson bombed down the left and delivered into the area for Zoko who saw his powerful volley touched on to the crossbar by Chapman.
This initiated a rise in the decibel levels at Huish Park as the Thatchers Terrace choir strained their vocal chords.
It spurred the Green and Whites on for more glory in the first period and they deservedly went ahead.
Khan’s deep cross found Rhys Browne at the back post, and he unselfishly nodded back inside for Zoko to score at the second time of asking.
Almost immediately after Accrington got the game going again, Yeovil netted their third.
Captain James Bailey played a delightful, lofted ball over the top for Olomola to run on to and he made no mistake in lifting it over an onrushing Chapman.
Stanley threatened to reduce the deficit seconds following the interval. A surging downfield run from Kee ended in Jordan Clark firing low at Krysiak.
Former Burton Albion forward Kee, renowned for his goalscoring ability, turned provider once more as the Lancashire outfit added their second.
The 26-year-old’s slide-rule pass was gathered by strike partner Jackson who curled into the bottom corner with aplomb.
Accrington would have levelled on the hour mark if not for the heroics of Krysiak.
The Polish keeper made a flying save to push Clark’s header on the bar and followed up with a similar stop to deny Mark Hughes from the resulting corner.
His counterpart Chapman was in fine form to prevent Khan’s free kick from nestling in the top corner before the ex-Barnsley man’s dazzling slalom concluded with a venomous shot tipped over.
Zoko had a chance to wrap up the match in the closing stages but fired over, however the damage was already implemented as far as Yeovil concerned – a good way to kick-start their league campaign.
Yeovil Town: Krysiak, Mugabi, Sowunmi, N.Smith, Dickson, Browne, C.Smith, Bailey, Khan, Zoko, Olomola (Surridge 80). Not Used: Maddison, Alfei, James, Davies, Gray, Santos.
Accrington Stanley: Chapman, Forbes (Ogle 46), Hughes, Donacien, Dallison (McLeod 89), Clark, Nolan, Conneely, McConville, Kee, Jackson. Not Used: Bloch Jorgensen, Richards-Everton, Brown, Sousa, Edwards.