In a heart-stopping finish, a long shot by Aaron Davey from beyond 50 metres in the last minute was touched on the line by Adelaide's Trent Hentschel, avoiding a potential draw between the clubs.
The thrilling contest was the first match played for premiership points at the venue since August 1992 and was enthusiastically supported by 8258 spectators who saw the Crows bring up their second win for the season while the Demons remain winless after three rounds.
Twice Melbourne came back from more than 30-point deficits but the Dees' plucky display just fell short as the Crows prevailed 15.12 (102) to 14.13 (97).
Melbourne started the final term trailing by 25 points and kicked the opening goal of the courtesy of a great snap by skipper David Neitz to bring up his third for the match.
Nathan Brown, who had worked tirelessly running out of defence, added his second another minutes later, but when Simon Goodwin found Ricciuto at the 16-minute mark in front of goal, the skipper converted and gave the Crows a 17-point buffer.
Neitz then landed his fourth to keep his side within touch and Brad Green had an opportunity to close the margin further, but just missed to the left with his snap at goal.
At the 25-minute mark, Brown found Cameron Bruce who kicked truly to make it a one-goal deficit before Davey's long shot attempt found Hentschel's fingertips on the way through.
Adelaide's midfield - led by Simon Goodwin with 34 possessions, including 12 in a frantic last quarter - proved the difference along with teammates Tyson Edwards (27) and Andrew McLeod (19), and continually drove the ball forward where their small forwards were able to make the most of numerous opportunities.
Jared Rivers tried hard in his return to senior football as he kept Adelaide's tall forwards in Ian Perrie and Henschel who, besides his match-saving effort in defence, managed one goal.
Brown, with his two goals and 24 possessions, was one of the Demons' best while Bruce lifted after the main break to be a main contributor and Brock McLean picked up 24 touches.
Byron Pickett added some much needed strength around the packs while Aaron Davey showed glimpses of his dash but was forced to gather the ball a long way from goal.
The game began with Adelaide capitalising on having first use of the breeze to the northern end of the ground courtesy of Brett Burton who booted four goals for the term.
The lively forward kicked the opening goal in the first minute of the match before bouncing through another three while seeing off three separate opponents as Neale Daniher attempted to stem the tide.
Melbourne, through Queenslander Brad Miller, had replied instantly to Burton's opener then followed with another through Brown who was playing as a loose man in defence before the 'blond-haired birdman' put on his display.
Matthew Bode was also proving elusive on the Crows' forward line as he helped himself to two goals as the Crows established a 29-point lead at the first break.
The second quarter went for 33 minutes and was the best of the game with both sides combining for a 12-goal feast.
Melbourne answered Daniher's urgings at the top of the term kicking two quick goals through Bruce and Aaron Davey to briefly narrow the margin.
Goals were then exchanged between Hentschel and Neitz before Ricciuto found his range and answered with two majors of his own in quick succession, including a brilliant snap from the forward pocket.
The captain's efforts seem to spark the Crows who kicked away to a 38-point-lead at the 22-minute mark after Bode added his third goal for the game and Hayden Skipworth his first.
To its credit, Melbourne finally awoke from its slumber and perhaps sensing the Crows were thinking about half-time, the Dees piled on four goals in the last eight minutes to get themselves back into the game at the main break.
Russell Robertson began the fight back with one of his trademark leaps over Nathan Bassett to pull down a spectacular mark and converted from 35 metres out, followed by quick goals from Bruce, Adam Yze and Travis Johnstone ended an entertaining term with a great effort on the run.
However, Adelaide came out full of running at the start of the third quarter and two rapid goals from Tyson Edwards followed by Burton's fifth and the Crows had skipped away again to 33-point lead and it proved too much for Melbourne despite coming home with the breeze in the final quarter.
The Demons had their chances late in the third term but despite a team lifting individual effort by Neitz - Melbourne's only goal for the quarter - they could only manage a rally of behinds including a missed set shot opportunity on the siren by Bruce.
As expected, the only change before the game was made by Adelaide with Martin Mattner failing to come up with his calf injury with on-baller Kris Massie as his replacement.
Adelaide coach Neil Craig described the narrow victory as a 'really good win' and praised his team's resilience.
"Our ability to respond from last week gives our guys a lot of belief in their resilience," Craig said.
"To come up here and play - because it is a long way to travel - having not seen the venue before so you put all that together and the motivation Melbourne had - well, it was a fantastic win for us."
Melbourne coach Neale Daniher was naturally disappointed his team came so close to their first win of the season and despite their persistence, he blamed costly defensive errors for a game 'we could have won.'
"Probably more disappointed with our second quarter to give them five (goals) and a lot of those were our own errors," said Daniher.
"We lost because we gave them goals from our own errors and a lot of wounds were self inflicted.
"We showed some really good signs in a sense of being competitive and hanging in there but just fell short."
MELBOURNE: 2.0, 9.5, 10.9, 14.3 (97)
ADELAIDE: 6.5, 11.6, 14.10, 15.12 (102)
GOALS - Melbourne: Neitz 4, Bruce 3, Brown 2, Robertson, Miller, Yze, Johnstone, Davey
Adelaide: Burton 5, Bode 3, Ricciuto 3, Edwards 2, Hentschel, Skipworth
BEST - Melbourne: Brown, Bruce, Rivers, Pickett, Green, McLean, Johnstone
Adelaide: Goodwin, McLeod, Edwards, Burton, Bode, Ricciuto, Reilly
INJURIES - Melbourne: Nil
Adelaide: Nil
CHANGES - Melbourne: Nil
Adelaide: Mattner (calf) replaced in selected side by Massie
REPORTS - Nil
UMPIRES - Stevic, McLaren, Jeffery
CROWD - 8,258 at Carrara Stadium
