Butters (37 disposals) and Horne-Francis (29, one goal) dominated as the unfancied Power triumphed 13.19 (97) to 11.5 (71) at Adelaide Oval on Saturday night.
Forwards Corey Durdin and Mitch Georgiades kicked three goals each and Joe Berry and Jase Burgoyne two apiece as the 15th-placed Port stunned the fifth-placed Crows.
Butters and Horne-Francis were superb as Port controlled the clearances 42-22. The pair recorded 13 and 10 clearances respectively, more than the entire Adelaide team.
"It's one of the best wins I have been involved with at the footy club," Butters said.
Port seized command with a stretch of six consecutive majors from midway through the second term, turning a three-point deficit into a commanding 35-point lead early in the third quarter.
Adelaide, now with nine wins and six losses, blew a chance to rise to fourth on the ladder.
"Just a really poor night, about as poor as we've been, unfortunately, this year," Crows coach Matthew Nicks said.
Crows attacker Darcy Fogarty booted five goals in a lone attacking hand - his captain Jordan Dawson was subdued despite collecting 25 disposals, and key teammates Izak Rankine (12 touches) and Josh Rachele (nine possessions, one goal) failed to fire.
Adelaide ace Rankine limped off late in the first quarter after his right leg was trapped in a Butters tackle.
Rankine's absence came as Port won the clearances 16-4 in the opening term but failed to cash in on the scoreboard.
The Power sprayed three set shots at goal and the Crows, with Rachele bouncing through a 40-metre stunner from near a boundary line in a rare Adelaide highlight, led by four points at quarter-time, 4.2 to 3.4.
Rankine returned to action with his right knee strapped in the second term as the Power seized momentum with five goals to two for the quarter.
Port's small forwards Berry and Durdin slotted two goals each in the quarter as their side skipped 16 points clear at halftime, 8.6 to 6.2.
The Power streeted 36 points clear with the initial three goals of the third term in front of a raucous crowd of 50,087 spectators at Port's nominal home game.
Port held a decisive 33-point advantage at three-quarter time, before closing out victory to narrow the overall win-loss ledger to 29-31 in Adelaide's favour.
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