Having left Upton Park, their home for the past 112 years, in the summer, West Ham were starting a new era in a stadium that hosted athletics at London 2012.
Any concerns the unfamiliar surroundings would hamper Slaven Bilic’s side were quickly dispelled, largely thanks to Kouyate’s two goals in 17 first half minutes.
The Hammers were greeted with a rendition of ‘I’m Forever Blowing Bubbles’ from the sell-out crowd as they emerged from the tunnel.
They then stylishly turned a 2-1 deficit into a 4-2 aggregate win four years to the day Jessica Ennis, Greg Rutherford and Mo Farah all won Olympic gold at the venue for Great Britain.
Senegal midfielder Kouyate clearly enjoyed his new surroundings and his double dispersed any nerves the home side might have been feeling.
Algeria winger Ferguli, a free transfer after six seasons at Valencia, rubber-stamped a comprehensive win on his home debut with a neat finish following Mark Noble’s threaded pass.
Who next for the Hammers?
West Ham must clear one more hurdle to secure a place in the Europa League group stage.
They will join 43 other clubs in Friday’s play-off round draw, which includes 15 losers from the 2016-17 Champions League third qualifying round.
The Hammers enter the draw as one of the seeded teams and could face, amongst others, Grasshopper Zurich, Danish club Brondby and Astra Giurgiu, the Romanian team who knocked the Hammers out at the third qualifying round stage of last season’s Europa League.
Aberdeen were left to rue a missed penalty, refereeing decisions and an own goal as they were knocked out of the Europa League by NK Maribor.
Adam Rooney’s spot-kick was saved, but if the advantage had been played Niall McGinn’s netted shot after the foul on Rooney would have opened the scoring.
Dons substitute Jayden Stockley was booked twice for use of his elbows.
And, in added time, Graeme Shinnie’s pass-back to Joe Lewis bobbled over the keeper’s foot and ran into the net.
The tie was played against a backdrop of mourning, after two players from Maribor’s B team – Damjan Marjanovic and Zoran Baljak – died in a car crash earlier in the week.
A minute’s silence before kick-off and black armbands were symbols of the sense of grief that had gripped the Slovenian club, and there was empathy from Aberdeen’s players and staff, with manager Derek McInnes and captain Ryan Jack laying a wreath earlier in the day.
Aberdeen’s task was straightforward – to score after conceding an away goal in the 1-1 draw at Pittodrie last week.
They travelled to Slovenia with a sense of purpose and confidence, though, having created a series of chances in the home leg and played with command and authority.
The loss of first-leg scorer Jonny Hayes to injury was a setback but his replacement Wes Burns brought drive and directness to the team, qualities which contributed to the conservatism that shaped Maribor’s play.
The home side could afford to play for a 0-0 draw, but they ought to have found themselves chasing the game by half-time.
A reckless pass-back by Marko Suler was intercepted by Rooney and his ankles were caught by Handanovic’s studs.
The referee opted for a yellow rather than a red card for the goalkeeper, but also ruled out McGinn’s finish to award the spot-kick instead.
Rooney, normally so fierce with his finishing from the spot, tried to dink the ball down the centre of goal, allowing Handanovic to kick the ball away.
There were other efforts – Burns and Shinnie both shot straight at Handanovic – but Aberdeen were most frustrated by the officials.
Even before Burns’ second-half replacement Stockley had received his two bookings, Erik Janza was only shown a yellow card despite appearing to have thrown a punch at Ryan Jack.
The home side had started the second half with more assertive play, and threatened when their scorer in the first leg, Milivoje Novakovic, spun and shot on target only for Lewis to push the ball away.
Aberdeen would still have felt they were the dominant side, but Stockley’s dismissal limited their options and it became an agonising assignment for the visitors as time ran out on their European ambitions, Shinnie credited with the own goal that came seconds before the final whistle.
Derek McInnes’ men – Scottish Premiership runners-up two years running – bow out of the Europa League at the third qualifying round for the third successive season, with their domestic campaign beginning at St Johnstone’s McDiarmid Park on Sunday.