The South African pace bowler, who played 15 games for Derbyshire last year in all cricket, delivered a disastrous over – the 12th of the innings – which cost 32 runs and was the turning point in a thumping defeat.
Prior to that, Derbyshire –sent into bat beneath cloudy skies – were no better than usefully placed at 96-2 having lost both openers to poor shots – Luis Reece top-edging an ugly cross-batted hoick to mid-on, and captain Billy Goldeman strangled down the leg-side.
But after Olivier’s third and, predictably, last over of the piece was pulverised, and after fellow South African Keshav Maharaj, the left-arm spinner making his T20 debut for the club, conceded 13 off the next over, Derbyshire’s score had skyrocketed from 96-2 to 141-2 in the space of two overs, enabling the visitors to reach a final total of 207-5.
Faced with such a stiff target, Yorkshire’s task was not assisted by the loss of the three men most likely to help them achieve it inside the first 3.4 overs of their reply.
Tom Kohler-Cadmore slapped to point, David Willey sliced to third man, and Adam Lyth was caught behind trying to drive through the covers to leave the hosts 40-3.
There were useful cameos from Jack Leaning, who top-scored with 36 from 30, and Jordan Thompson, who struck 23 from 12, but wickets tumbled towards the end as Yorkshire lost their last five for 18 to be bowled out for 152 with 2.5 overs of their innings unused.
Derbyshire’s 55-run triumph saw them maintain the Indian sign over Yorkshire in this form of cricket, with their sixth successive T20 win against the White Rose consigning Yorkshire to the bottom of the North Group, the position that Derbyshire had occupied beforehand.
Olivier, the 27-year-old who controversially quit international cricket to sign a three-year Kolpak deal in February, had been a hit-and-miss figure throughout the summer.
Although he has taken plenty of wickets and forced almost as many concussion checks in the process, he has had a tendency to be more expensive than a luxury watch, and so it proved again as Leus du Plooy – his former Free State team-mate – took him apart.
The left-hander clubbed the first ball of Olivier’s fateful over from the Kirkstall Lane end for six over long-off, which was also a no-ball on height so cost eight runs in total.
Du Plooy then hit the free-hit for six over mid-wicket, and, after taking three runs and his partner Wayne Madsen a single, finished the over by smashing Olivier for a two-bounce four over mid-on, a pulled six and a four through the covers, the momentum of the contest utterly transformed.
Du Plooy reached a blistering half-century from just 20 deliveries, Madsen following him to the landmark from 31 balls, the pair sharing a decisive fourth-wicket stand of 87 in seven overs.
Madsen went on to the top score off 66 from 37, and du Plooy to 51 from 23, both men trapped lbw by Tim Bresnan and Willey respectively.
Bresnan – held back until the 17th over – was the pick of the attack with 2-17 from two overs, the former England all-rounder also having Matt Critchley caught at point.
Yorkshire fielded three spinners in the form of Maharaj, Dom Bess and Jack Shutt, who bowled eight wicket-less overs between them for 79.
Du Plooy especially caught the eye before a crowd of around 8,122, but Madsen’s performance was no less muscular and, like his partner, he struck four sixes.
Madsen also scooped a couple of boundaries over the wicketkeeper’s head and displayed great dexterity to go with the ability to strike the ball a long distance, aided and abetted by fast wrists and footwork.
Madsen offered one chance, dropped on 28 when he sliced Olivier to third man with the score on 83-2 in the 10th over.
It was a difficult opportunity, the ball swirling in a stiff breeze as it sailed out to Shutt in front of the new stand, and who knows whether it would have made a difference to the end result.
After the quickfire loss of their top-three batsmen, Yorkshire had it all to do to get anywhere close to Derbyshire’s score.
Leaning, Jonny Tattersall and Jordan Thompson at least threatened to make a game of it, but once Thompson was caught at cover in the 14th over, leaving Yorkshire 134-6, the writing that had long been on the wall was now illuminated in dazzling light.
Logan van Beek, the pace bowler, finished with a T20 career-best 4-17 from three overs, and Yorkshire finished with a familiar headache as to how a side which, on paper, has talent aplenty, cannot translate it into consistent results in the game’s shortest format.
Remarkably, and despite now propping up the rest of the division, they remain only three points off the top-four qualifying places with five games left, a reflection, perhaps, on the number of no-results that have been knocking around due to the weather, but it would take something truly special now for Yorkshire to qualify.