The England midfielder doubled Spurs' lead at The Emirates Stadium with a delightful goal after Harry Kane's through pass, to confirm the 2-0 win.
Victory sets up a two-legged last four clash with Chelsea for a place in the final at Wembley as Mauricio Pochettino eyes his first major trophy.
It was Tottenham's first win at Arsenal since 2010 and came after Unai Emery's side came from behind to prevail 4-2 in their Premier League encounter earlier this month.
And the extra special result was particularly enjoyed by Jenas, who documented his reaction during a flurry of posts to his Instagram story.
The BBC and BT Pundit made over 200 appearances for Tottenham during eight seasons at the club and was part of the last squad to win a major trophy, when they scooped the Carabao Cup in 2008.
Son Heung-Min put the visitors into a half-time lead which was cemented thanks to Alli's cute finish just prior to the hour mark after substitute Kane's chipped pass – which followed his assist in the weekend win over Burnley.
Jenas reacted: "Man like Dele. Another assist from H [Kane], another assist.
"It’s beautiful, stop it. You can’t keep giving assists like this Harry, oh my God. Oh my God."
Additional footage captured during 22-year-old Alli's goal showed Jenas running around in celebration and shouting "what a f***ing goal that is".
On Twitter, the ex-England international added: "That's just ridiculous."
Alli's contribution was later overshadowed after a bottle thrown from an Arsenal fan struck him on the head.
The Gunners, Metropolitan Police and The Football Association are all investigating the incident which is the latest intervention from a supporter in recent weeks.
Pochettino was relieved that Alli was left unhurt and called on Arsenal to take action against the offending supporter.
He told the media: "I saw it and it was lucky that it wasn’t a big issue.
"We play a derby and we hate each other in a good way but it is in a bad way when you go to damage some people or an opponent. It is only one stupid person who made a mistake.
"I respect the Arsenal fans. For one [fan], you cannot talk about everyone.
“I hope that Arsenal take responsibility and, through the cameras, they can identify [who it was] because it wasn’t a problem but it could have been a big problem, some big issue and how are we going to fix it?”
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