And Melbourne will doubly count the cost of the loss, with superstar Juan Mata potentially hyperextending his elbow after slipping awkwardly and wearing heavy strapping on Sunday.
Having not won against the Victory in Melbourne since 2017 the visitors, who had several players battling illness or injury during the week, were poised to continue their drought and settle for a 0-0 stalemate.
A draw would have been a missed opportunity after the Phoenix had countless opportunities and dominated large parts of the contest, frustrating a Victory side who couldn't overcome their opponents' rigid defence.
But 16 minutes after coming on, Kartum found Wellington's deserved goal in the 89th minute when a lofted cross from Ifeanyi Eze found the Norwegian import on the right of the penalty area and he volleyed the ball in via the left post.
The result keeps Wellington's finals campaign alive as they move within one point of the sixth-placed Macarthur FC (31 points).
"We've had a few niggles throughout the week if I'm honest. Bill Tuiloma has been pretty sick for two or three days, and I thought he was a warrior out there for us today," interim coach Chris Greenacre said.
"Isaac Hughes had a concussion and was touch-and-go for part of the week.
"It makes that win today even more important when we know what's going on behind the scenes."
For Melbourne, they'll wait for scans on Mata, said by coach Arthur Diles to have been in considerable pain.
But to make matters worse, Victory's hopes of claiming the Premier's Plate are all but dashed with three games remaining.
A win would have brought them within two points of the second-placed Auckland (40 points), who they play next round.
The Kiwis are only three points behind the ladder-leading Newcastle (43 points), who the Victory play in the following week, meaning three points from all three matches would lay the platform for a late run at the premiership.
But after the loss, the Victory now sit eight points away from Newcastle.
"We were cheap on turnovers. It just wasn't us," Diles said.
"It was very hard to find our flow and our rhythm in that first half. It was probably our worst half of football this year."
Wellington had an early chance go begging when Corban Piper met a cross at the back post but clattered his shot into the crossbar.
Kartum gave the visitors the lead with his strike and the Phoenix withstood a desperate Melbourne to win.
