Former Storm star Brett Kimmorley kicked the winning field goal from 35 metres out in the 79th minute, but the major talking points were the sendings-off of Ross and Melbourne counterpart Brett White.
Ross got his marching orders from referee Tony Archer for elbowing Cronk in the head just after the Storm halfback had kicked to Israel Folau for Melbourne's third try which levelled the scores at 16-16 in the 65th minute.
White was sent off for retaliating and punching Ross in the head.
It continued an eventful start to the season for Ross, who lost three teeth and suffered heavy concussion in a heavy head clash with Manly's Josh Perry last week.
He was also involved in a similar incident last year, when he was suspended for three weeks for a grade five reckless high tackle on Bulldogs forward Kane Cleal.
If Sunday's incident is considered a grade four offence by the match review committee, Ross could be hit with a 50 per cent prior similar loading, in addition to 75 carryover points from the Cleal incident.
Or the matter could be referred straight to the judiciary.
White is also looking at a suspension after collecting Ross with two punches to the head.
"Obviously it was late and (Ross) had his elbow up," said Melbourne captain Cameron Smith.
"They brought in a rule to take out the late hits on kickers and obviously the referee was right there."
Cronulla coach Ricky Stuart refused to comment until he had seen footage of the incident.
Kimmorley felt it was fair that both Ross and White were sent off.
"I think both of those incidents were as bad as each other - Benny's shot on Cooper but also the shot on Benny," he said.
"I think they are as bad as each other so whatever one should get the other should get."
Kimmorley revealed he had stayed behind for extra field goal practice on Saturday night and it paid dividends, as he slotted the game winner in the 79th minute shortly after Cronk had missed at the other end.
It was Melbourne's first home loss since going down to the NZ Warriors 18 months ago.
The Sharks have now beaten both of last year's grand finalists in the opening two weeks, while the result was sweet revenge for a 17-16 home loss to Melbourne last year after leading 14-0.
Centre Russ Aitken got Melbourne on the scoreboard in the 15th minute, taking a fine pass from Cronk and crashing over with three Sharks defenders on his back.
White scored Melbourne's second try in the 20th minute, barging through the Sharks' defensive line.
The second half was a war of attrition.
Luke Covell kicked a 62nd minute penalty goal for the Sharks, only for Folau to level the scores at 16-16 in the play which led to the sendings-off of Ross and White.
"I'm still a bit disappointed about how we have so many unprofessional turnovers," said Stuart.
"It's too much disrespect for the football and makes it so much hard work for ourselves.'
"(But) I'm over the moon about the result because I know how every game counts towards a semi-final berth."