Frances Tiafoe threw up during his first-round match at the Australian Open along the way to a five-set victory and said afterward he might have quit if this had been just a run-of-the-mill tournament.

Once leading Arthur Rinderknech by two sets, the No. 17 seed found himself in a decider after a testing turn of events. Up 5-2 in the fourth set, Tiafoe couldn’t close out the Frenchman when it ...