Newly crowned European champion Italy produced a dominant performance as it thrashed Lithuania 5-0 in the World Cup 2022 qualifiers Wednesday.
European runner-up England, on the other hand, was forced to settle for a draw in Poland.
Italy had drawn its previous two qualifiers to slip into a battle with Switzerland for automatic qualification from Group C.
But the Azzurri, who set a new world record of 36 internationals unbeaten with the goalless draw against the Swiss at the weekend, produced a dominant display against Lithuania in Reggio Emilia.
Young striker Kean, who rejoined Juventus from Everton in the close-season after a successful loan spell at Paris Saint-Germain, scored twice in the first half.
Edgaras Utkus put through his own net and Giacomo Raspadori also scored as Italy moved four ahead at the break.
Giovanni Di Lorenzo made it five in the second period as Roberto Mancini's side stretched its lead over Switzerland at the top of the table to six points.
"It was important to have won this game with young players, who played very well, especially in the first half," Mancini told RAI.
"They (Kean and Raspadori) have a great future, everything will depend on them."
Italy is hoping to banish the memories of its shock failure to qualify for the 2018 World Cup in Russia.
The Swiss do have two games in hand, but they were held to a 0-0 draw by Northern Ireland in Belfast, with Haris Seferovic having a penalty saved by Bailey Peacock-Farrell.
England, who was beaten by Italy on penalties in the Euro 2020 final at Wembley, lost its 100% record in qualifying with a 1-1 draw against Poland in Warsaw.
The hosts were second in Group I, five points behind England, before kick-off and frustrated its opponent for long periods.
England captain Harry Kane appeared to have settled a tempestuous affair with 18 minutes remaining, slamming a swerving long-range shot into the bottom corner to score his 41st international goal.
But Szymanski headed home at the back post from Robert Lewandowski's cross in injury time.
"A tough one to take right at the end," Kane told ITV. "Sometimes the pressure comes away from home but we are top with four games to go."
Gareth Southgate's men are still four points clear of second-placed Albania, who thumped San Marino 5-0 in Tirana.
Spain's qualification hopes were under threat heading into its game at Kosovo, but a 2-0 win, coupled with Sweden's surprise loss to Greece, gave Luis Enrique's side a much-needed boost.
West Ham United midfielder Pablo Fornal's 32nd-minute strike and Ferran Torres' late goal gave the 2010 world champions all three points in Pristina.
Sweden, albeit having played two matches fewer than Spain, slipped four points adrift of its Group B rivals after a 2-1 defeat by the Greeks.
Germany entered the current international break with a new coach, Hansi Flick, and looking to hit back following its European Championship last-16 exit at the hands of England, just months after a shock World Cup qualifying home loss to North Macedonia.
But an impressive 4-0 victory in Iceland made it three wins from three for the former Bayern Munich boss.
There had been serious questions marks raised about the form of forwards Timo Werner, Serge Gnabry and Leroy Sane, but all three netted in Reykjavik.
Werner and Gnabry have both scored three times in these three games, with Sane on the scoresheet twice.
Chelsea center back Antonio Ruediger was the other scorer as Germany stretched four points clear of Armenia in Group J.
The Armenians were held to a disappointing 1-1 home draw by Liechtenstein.
In Group E, Belgium continued its cruise towards qualification as Dennis Praet's first-half effort saw Roberto Martinez's side edge out Belarus 1-0 in Kazan.
Wales is now nine points behind the Red Devils after a goalless stalemate with Estonia in Cardiff.