With the tie locked at 1-1 from the first leg in London last week, Solanke kept his cool from 12 yards in the first half at Deutsch Park to secure a 2-1 aggregate triumph.

Fares Chaibi and Rasmus Kristensen missed big second-half chances for Eintracht as Spurs held on for a priceless win.

Victory in this quarter-final tie eases some of the pressure on under-fire boss Ange Postecoglou, who knows winning this tournament might be the only way to keep him in the Spurs job.

Micky van de Ven made a fantastic last-gasp tackle to deny Hugo Ekitike one-on-one after 15 minutes, while Kaua Santos saved Mathys Tel's long-range bending effort.

But Santos was punished for clattering into James Maddison after referee Davide Massa consulted the video assistant referee and Solanke sent his spot-kick straight down the middle two minutes before the break.

Chaibi had Guglielmo Vicario scrambling with an excellent 30-yard free-kick shortly after the restart, while Cristian Romero planted a header wide from a Spurs corner at the other end.

Vicario then pulled off an exquisite save with his legs when Chaibi met Kristensen's near-post cutback, with the latter missing a gilt-edged chance when he bent wide from 10 yards as Spurs clung on amid heavy second-half pressure.

Postecoglou does not envisage his doubters being silenced despite Tottenham's win, though.

"I said yesterday I'm the same coach today that I was yesterday and my pleasure just comes from watching this group of players rewarded.

"They've never lost belief, the staff and players never have."

Asked what impressed him most against Eintracht, Postecoglou added: "Just the togetherness of the lads, it's fair to say there's been a fair bit of noise around the team but you wouldn't know it.

"They didn't care, they've just been so focused on us achieving what we want to and I'm super proud of them.

"The travelling fans were brilliant tonight, hopefully they enjoy it, they deserve it. Our fans have been through a lot too and we understand their disappointment.

"But hopefully this just gives them something to look forward to."

Tottenham now faces Norwegian outfit Bodo/Glimt in the semi-finals after a dramatic penalty shootout win over Lazio.

The Serie A giant, trailing 2-0 from the first leg, levelled the tie at two-apiece with Tijjani Noslin scoring deep into stoppage-time at Stadio Olimpico.

It looked as though the hosts were going through when Boulaye Dia put Lazio ahead but Andreas Helmersen restored parity once more then was sent off in the last minute of extra-time, before the visitors went on to win on penalties 3-2.