Demons star Christian Petracca's shot from outside 50m was initially ruled touched on the goal line by Caleb Marchbank and officials found insufficient evidence to overturn the umpire's soft call on review.
Melbourne had time for two more entries into a crowded forward line in the final 30 seconds but were unable to find a winning score, with the Blues hanging on for a 9.6 (60) to 8.8 (56) triumph.
It keeps Michael Voss's side in fifth spot with two rounds left to play and means the Demons slip to third, replaced in the top two by Brisbane.
The Blues are now almost certain to end a decade-long finals drought, having seemed out of contention at the halfway point of the season.
Patrick Cripps (29 disposals, five clearances) and George Hewett (33, eight) stood up for Carlton in an undermanned midfield, while Nic Newman, Adam Saad and Jacob Weitering all played important roles.
Blues spearhead Charlie Curnow booted two goals in the low-scoring contest, taking his tally to 70 in a career-best season that is likely to end with a second Coleman Medal hung around his neck.
Matt Owies also kicked two crucial goals.
Petracca (24 disposals, two goals) almost hauled Melbourne over the line with Jack Viney (31 touches, five clearances) and Angus Brayshaw (31, seven) busy.
Clayton Oliver had 27 disposals and nine clearances on return after an extended lay-off with hamstring issues, while big-name recruit Brodie Grundy (nine touches, 11 hit-outs) didn't have a huge impact after being recalled.
It was Carlton's game early - only without reward on the scoreboard.
The Blues failed to convert their territorial dominance, taking a measly three-point lead to quarter-time from a lopsided 24-4 inside-50 advantage.
It had grown to 27-6 by the three-minute mark of the second quarter when the Demons' quick transition led to a Kade Chandler goal that put them in front against the tide.
The margin never got to double figures either way in a dour first half, with Melbourne livewire Kysaiah Pickett's soaring mark over Alex Cincotta a rare highlight.
Carlton kicked three of the first four goals after the main break but scores were locked at 42-42 by three-quarter time as the arm wrestle continued.
Goals to Matt Owies and Tom De Koning in the opening two minutes of the final term put the Blues in the driver's seat again before Curnow's second gave them an 18-point lead - the biggest of the night.
Goals to Pickett and Joel Smith dragged Melbourne back within a kick before Petracca's late effort fell short.
A crowd of 68,577 was on hand at the MCG, with many fans packing the concourse and bars during a dour first quarter to watch the Matildas' penalty shootout win over France on TV screens.
