England achieved their most emphatic World Cup result as Harry Kane's hat-trick helped them thrash a poor Panama side and reach the last 16.
There were five first-half goals, with John Stones heading in the opener.
Kane made it 2-0 from the spot before Jesse Lingard, who was fouled in the box, made it 3-0 with a great strike.
Stones nodded in his second, Kane smashed in another penalty and then scored a lucky third, before Felipe Baloy fired in a consolation goal.
This was the first time England had scored four goals in a World Cup match since the 1966 final against Germany.
Meanwhile, skipper Kane, who now has five goals in the tournament, became the third England player to score three or more goals in a World Cup group stage, after Roger Hunt in 1966 and Gary Lineker in 1986.
England will now compete with Belgium - who secured their second win by beating Tunisia 5-2 on Saturday - for top spot when they play each other on Thursday (19:00 BST).
Ruthless England sparkle in the sun
World Cup 2018: John Stones puts England 1-0 up against Panama
England's opening win over Tunisia contained one serious flaw that needed correcting - namely a lack of ruthlessness and clinical edge in front of goal.
As Panama were totally dismantled, the failing was addressed and them some as a place in the last-16 stage was secured in quick-fire fashion.
Strangely, England had actually made a subdued and sloppy start before Stones powered in Kieran Trippier's corner to put them ahead. It was plain sailing from then on.
Southgate's side sparkled in Nizhny Novgorod, pace and movement mixed with flashes of individual brilliance such as Lingard's goal to reduce Panama to an ill-disciplined shambles.
When they get it right, England have the firepower to trouble any team, with captain Kane a spearhead approaching world class.
They also showed commendable first-half discipline to avoid getting involved in Panama's ham-fisted physical approach, simply letting the inevitable take its course in the hands of Egyptian referee Ghead Grisha, who was determined to punish penalty-area transgressions.
England inevitably eased off with the game and that place in the last 16 no longer in doubt, and of course greater tests lie ahead. But this was the sort of commanding performance that will do wonders for confidence as the World Cup reaches the knockout stage.