The defending champions have just one win from six matches and a loss to Australia in Ahmedabad on Saturday will confirm that their meek title defence is over.
Stokes took to social media in the middle of the night to make it clear there was no snub intended because England players eventually met up with their Australian counterparts at a nightclub.
"Another wonderful game, right down to the wire," Cummins said. "Stokesy gave us a few heart-stopping moments and the crowd seemed to enjoy it."
Batting in partnership with fast bowler Mitchell Starc, Lyon, playing in his 100th consecutive test match, looked like a sitting duck as he fended off some hostile bowling
Usman Khawaja was the pick of the batters, racking up 58 not out, while England's bogeyman Steve Smith was on six when the rain brought the day's play to an end
As commentator Daniel Norcross told the BBC: "He is the scourge of the English. He is the modern-day Bradman."
Head joined Smith and accelerated the scoring rate as the England bowlers tired in the final session
Australia won the opening Test at Edgbaston by two wickets after England skipper Ben Stokes had declared his team's first innings at 393 for eight.
An unbroken ninth-wicket stand of 55 between Australia captain Pat Cummins and Nathan Lyon on Tuesday's final day proved decisive in a see-saw contest as the tourists chased down a target of 281