- England have lost just one of their last 20 internationals at Wembley (W15 D4), losing against Netherlands in March 2016 - the Three Lions have been unbeaten in their 10 games at the National Stadium since (W6 D4).
The goal came on 87 minutes, after a VAR consultation from referee Deniz Aytekin rightly adjudged debutante James Tarkowski to have trodden on Federico Chiesa's foot in the England box.
Jamie Vardy hit the opening goal in the 26th minute after good work from Jesse Lingard.
"I prefer the referee's decision is final".
James Tarkowski clearly seemed to trod on Chiesa for Italy's spot-kick, but even then England manager Southgate protested there wasn't sufficient evidence to overturn Aytekin's original decision.
England boss Gareth Southgate complained afterwards that the Tarkowski incident was not "clear and obvious", citing the guidelines for VAR where such a phrase actually does not feature.
Former England strikers Gary Lineker and Alan Shearer also voiced their displeasure. Shearer said on Twitter.
Replays suggested the VAR had made the right decision but the England manager, who had watched his team take the lead through Jamie Vardy's fine 26th-minute finish, felt guidelines that only "clear and obvious" errors should be corrected had not been followed.
Koreas fix date and place for historic summit
The two-day trip by Chinese State Councilor Yang Jiechi follows talks earlier this week between Kim Jong Un and Xi Jinping. The North's delegation is led by Ri Son Gwon , chairman of an agency that deals with inter-Korean affairs.
Lineker said: "It's irrelevant whether they think it was a penalty or not".
Even without injured Harry Kane his side looked lively in attack with Raheem Sterling finally beginning to look like a genuine threat at worldwide level.
England begin their World Cup campaign against Tunisia in Volgograd, Russia on June 18.
Alli, by contrast to Lingard, hasn't enjoyed his best season at Spurs and didn't start either against the Netherlands or Italy.
England's World Cup preparations continued in encouraging fashion despite the frustration of a video assistant referee ruling allowing Italy to snatch a 1-1 draw at Wembley.
Vardy's strike eased concerns about an attack which has been criticised for lacking goals in the absence of the injured Harry Kane, although it is now six games since they found the net a couple of times.
Kane has scored seven goals in his last six global appearances, but without the Spurs striker England lacked a cutting edge to kill the game off.
Southgate will have been largely impressed by his side's performance, although the three-man defence was guilty of the odd hairy moment - especially early on - and Jack Butland did not look as assured in possession as Jordan Pickford did on his audition for the number one jersey.