Both left the pits with left side wheels not fully attached, retiring shortly afterwards.
Haas team principal Günther Steiner, now hailed as a Netflix star even if he has yet to find time to watch the episodes, assured fans before Melbourne that the team had worked overtime on pit stop practice.
"It’s déjà vu," he agreed on Sunday. "We got [the wheel] on, but lost the positions anyway and then I think it was five or six laps later and this happened.
"It looks like just something broke when we put it on with sheer force the second time around."
Steiner could at least take consolation in Magnussen finishing sixth to send Haas fourth in the standings and ahead of Renault.
"The good thing I take away is that last year we went away last because we didn’t score any points," said Steiner. "This year we go away fourth, we are two points ahead of fifth.
"The car seems to perform very well. For sure we have to do the same in the next 20 races, but it seems to be solid, the drivers like it."