Having lost the first set 6-4, seven-time champion Djokovic was leading 4-1 in the second when fans burst into applause, leaving both players briefly puzzled before they saw the funny side of things.
Moments earlier, Trent Alexander-Arnold had converted the winning spot-kick in the shootout to send England into the last four after Manuel Akanji missed for Switzerland.
"I assumed it was a penalty shootout between England and Switzerland. It felt like for a set and a half the crowd really wanted to understand what the score was in the football match," Djokovic said shortly after sealing a 4-6 6-3 6-4 7-6(3) win.
"Did England win in the end? That's why you guys stayed. Congrats to England.
"I tried to shoot a penalty, I'm left-footed, but Alexei defended it well."