Having left Upton Park – their home for the past 112 years – in the summer, West Ham were starting a new era in the 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 first-leg deficit into a 4-2 aggregate win four years to the day Jessica Ennis-Hill, Greg Rutherford and Mo Farah all won Olympic gold at the venue for Great Britain on what has become known as Super Saturday.
Senegal midfielder Kouyate clearly enjoyed his new surroundings and his goals 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.
‘Atmosphere more than I expected’
West Ham manager Slaven Bilic: “It was difficult psychologically for us but for the stage we are at we played really well. We were fit, aggressive and played good football.
“We could have scored more goals, but it was a very mature performance. We played badly in the first leg but a week later we are fresher and closer to the season.
“I didn’t know what the atmosphere would be like. This was the first time we could judge it and it was more than I expected. It’s loud.”