Some of the criticism of Craig has been harsh.
In one rating block on the teams at the end of the drawn second test, Craig was given 3/10 with the accompanying words: "Is he the worst test spinner to ever be seen on Australian shores? How does he keep getting a game? Batsmen treat him with disdain and the only wickets he gets are cheap lower-order slog-outs when the opposition is looking to declare."
Another after Brisbane wondered if "grade cricket is his go".
Craig has been stiff a couple of times, notably having centurymaker Usman Khawaja caught behind off a big nick on 38 at the Waca, only for umpire Nigel Llong to give it not out, and New Zealand had no referrals left.
Craig did pick up wickets when batsmen were having a slog late in Australia's first innings in Perth, but coach Mike Hesson confirmed he is highly likely to play the decider at Adelaide Oval next week.
"Australia is a tough place to bowl spin," Hesson said.
"If you look at the stats there have been some high quality spinners that haven't done very well here. But what we've seen from him time and time again is that he has actually fought back for us."
Craig has won tests for New Zealand since his debut in the West Indies last year, when he took eight wickets in Jamaica to help set up a victory; and his 10 wickets against Pakistan in Sharjah bowled New Zealand to a big win late last year. In 12 tests he's taken 44 wickets at 44.5.
Hesson and Southee said Craig was coping with the criticism well.
"He's a pretty laidback character. No doubt he knows he's not bowling quite as well as he knows he can," Hesson said."
Craig's six wickets in the series have cost 72 runs apiece. By comparison, his Australian counterpart Nathan Lyon has taken seven wickets at 35.
Lyon, Australia's most successful offspinner with 169 wickets in 48 tests, has taken 24 in four tests at Adelaide at 28.2.