Essendon moved into the top four with the 19.14 (127) to 11.11 (77) win, its first against Port in Adelaide in 12 years.
The Bombers could still lose their place in the top four depending on other results over the the round.
The injury-prone Gumbleton, in his first match since late 2010, was influential as Essendon stunned the Power with a late surge.
The Bombers trailed by one point 24 minutes into the third quarter, but then kicked the final eight goals of the match.
Gumbleton and livewire Leroy Jetta (three goals) were prominent, while captain Jobe Watson and Dyson Heppell basked in the ruck dominance of Tom Bellchambers.
Port's Brett Ebert and Justin Westhoff each kicked three goals but the South Australian club remain in the mire with only four wins this season.
While Gumbleton was busy, his teammate Jake Carlisle will be scrutinised for a behind play bump on Port's Paul Stewart.
Carlisle floored an unsuspecting Stewart with a hip and shoulder 30m off the ball, forcing the Power forward from the field.
Stewart soon returned as both sides failed to steal momentum, with Port taking a two point lead into half-time, 8.6 to 8.4.
Essendon remained unable to shrug Port in the third term until ex-skipper David Hille booted two late goals.
Hille snapped across his body and then converted after a strong overhead mark to give the Bombers an 11-point break at three-quarter time.
Essendon, despite losing Michael Hibberd to an apparent thigh injury, then killed off Port with a final term flourish.
The Power were rendered helpless as the Bombers booted 6.5 to 0.2 for the quarter as Port crashed to its fifth consecutive defeat.
Hibberd's injury puts him in doubt for Essendon's meeting with reigning premiers Geelong on Friday night, Port plays fellow strugglers Melbourne next Saturday night in Darwin.
PORT ADELAIDE 4.3 8.6 11.9 11.11 (77)?
ESSENDON 4.2 8.4 13.8 19.13 (127)??
GOALS?
Port Adelaide: Westhoff, Ebert 3, D Stewart 2, McCarthy, P Stewart, Thomas
Essendon: Gumbleton, Jetta 3, Dell'Olio, Bellchambers, Hille 2, Davey, Dyson, Melksham, Reimers, Howlett, Myers, Watson
BEST?
Port Adelaide: Brad Ebert, Brett Ebert, Moore, Broadbent, Boak, Westhoff ?
INJURIES
Port Adelaide: ?Nil
Essendon: Michael Hibberd (quad)?
SUBS:
Port Adelaide: Matthew Lobbe replaced by Chad Wingard in the third quarter.
Essendon: Michael Hibberd (quad) replaced by Nathan Lovett-Murray in the third quarter.
Reports: Nil
Umpires: Farmer, Ritchie, Fila