Incidentally, he is the first player to have scored a brace and a hattrick in his two consecutive world cup outings, after Gary Lineker in 1985 World Cup finals.
The in-form Tottenham striker bagged his third after a 61st-minute shot by Ruben Loftus-Cheek hit his foot and bounced over despairing Panama goalkeeper Jaime Penedo.
England face Belgium in the final Group G match on Thursday night (1am Friday, Thailand time).
Even accounting for soft opposition in the World Cup debutantes and Tunisia before that, England's record so far contrasts starkly with four years ago when they were already eliminated after just two games in Brazil. "We wouldn't swap him for anyone in the tournament in terms of No. 9s", Southgate said. We can go into the Belgium game with confidence.
So if you had two incredibly cynical managers in charge of England and Belgium, both teams could play for a goalless draw and try to get their entire team, plus substitutes if required, booked, in an attempt to swerve the favourites.
"This is a top player, a world-class player - and we don't have many".
"We're not getting too ahead of ourselves", Kane said after the match.
Romelu Lukaku and Eden Hazard star as Belgium rout Tunisia
Belgium and England clash next Thursday in their final Group G match in Kaliningrad in a contest likely to decide the pool victor .
"I guess the bits in the middle were pretty good, but I am being hyper-critical", he said.
For England fans, the pain of being knocked out in the last 16 by Iceland in the 2016 European Championship and a first-round exit without a win at the 2014 World Cup, was finally slipping away.
"We knew before the game it would be aggressive, and they'd do everything they could to stop us".
They will then go on to the quarter-finals, where they will play either the runner-up or victor of Group H, depending on where they finish. If you want to achieve anything in life you have to believe. "England is totally spectacular, a attractive team", said Panama coach Hernan Dario Gomez, who went into the English changing room at half-time to congratulate Southgate. "We have got some decisions to make because the harmony of the group is important to me".
"They have some outstanding individual players", he said.