Morgan, who succeeded the dumped Alastair Cook for the six-week event, is in the midst of a slump which has seen him make just 0, 2, 0 and 0 again in his last four innings.
His latest disastrous outing was a duck in Wednesday's four-wicket loss to Pakistan in a warm-up game at the Sydney Cricket Ground, falling off a full toss from Yasir Shah.
"Morgs is one of the guys that under the pump, when the pressure is on, you turn to," Root told reporters.
"Everyone in the dressing room is absolutely convinced that's going to be the case. He scored a hundred not long ago. He's obviously a fine player, he's a fine leader."
Morgan came into the tournament under a cloud when it was revealed that he had been the target of a blackmail attempt over a relationship with an Australian woman five years ago.