Warren Tredrea booted the match-winning goal with just two minutes left on the clock.
A six-goal third quarter burst did the damage for the Port, which scored the most important victory in its five-year history 15.14.104 to 14.13.97.
The Bombers seemed lethargic early in the match with the effects of last weekend’s record-breaking comeback against the Kangaroos still taking their toll.
Port captain Matthew Primus headed a long list of Power players who performed strongly over four quarters in a win that ensured the side remained in the top four.
The Power jumped Essendon in the first quarter, with the Bombers’ two goals coming from soft 50-metre penalties and Port missing with some gettable scoring chances that could have had them further ahead.
Essendon fought back in the second quarter to take the lead by a point, and Scott Lucas kicked the first goal of the second half to put the Bombers up by seven points.
But Port Adelaide again stormed away, kicking the next five goals to set up a 25-point lead.
The Bombers charged back again in the last term, Matthew Lloyd booting three goals in the last quarter after being kept virtually out of the match for the first three terms by Stephen Paxman.
Essendon looked likely to win the match when Lucas kicked his third to level the scores 27 minutes into the final quarter.
But Primus won the next hit-out, which enabled Gavin Wanganeen to get a hurried kick forward for Tredrea's mark and goal.
Then Primus again set up the next centre clearance, which resulted in Stuart Dew kicking a behind which stretched the lead to seven points with only seconds left, sealing the win.
Sean Wellman was Essendon's best, with a good defensive effort as well as two goals when moved forward, while Jason Johnson continued his good form in the midfield.
Scoreboard:
PORT ADELAIDE: 4.5, 7.7, 13.9, 15.14 (104)
ESSENDON: 2.1, 7.8, 10.10, 14.13 (97)
Goals:
Port Adelaide: B Guerra 4, F Francis 2, C Cornes 2, W Tredrea 2, J Schofield, S Dew, J Carr, R James, N Stevens.
Essendon: M Lloyd 4, S Lucas 3, S Wellman 2, M Mercuri, M McVeigh, J Johnson, J Misiti, S Alessio.
Best:
Port Adelaide: M Primus, N Stevens, J Francou, G Wanganee,n S Paxman, B Guerra.
Essendon: S Wellman, J Johnson, P Barnard, S Alessio, S Lucas, J Hird.
Umpires: G Dore, D Goldspink, M James
Crowd: 37,930 at Football Park, Adelaide.
