Storm kicked off the inaugural NRL Double Header in front of 52,347 fans against North Queensland.
It was a game fitting off the big stage as the lead changed hands several times.
The Cowboys struck early before tries to Tohu Harris and Kevin Proctor, both in the space of three minutes, edged Storm into the lead.
Then with nine minutes to play, Storm skipper Cameron Smith put his side in front with a field goal in front of the posts to snatch the narrow victory.
That result proved Melbourne was capable of mixing it with the best sides in the competition.