Hodge was superb as the Hawks came from behind in the last quarter to win 13.11 (89) to 11.12 (78) at AAMI Stadium.
The Crows hit the front for the first time in the game when Scott Thompson goaled in the third minute of the last term.
But the Hawks responded with four quick goals to bank a fifth consecutive triumph.
Coach Alastair Clarkson said to notch a hard-fought win in enemy territory was "outstanding".
"They played some really good footy in the second quarter and got themselves back into the contest and then it was a real grind from that point on," Clarkson said.
"They're tough to beat in Adelaide ... to win in those circumstances, no matter what the margin is is an outstanding result for our club."
Skipper Hodge was instrumental with a best-afield 29-disposal performance, while Sam Mitchell, Jordan Lewis and Brad Sewell were all influential.
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Adelaide star Patrick Dangerfield turned in a brilliant two-goal, 35 possession game and Josh Jenkins, trying to fill the attacking void caused by Taylor Walker's injury, kicked 2.4.
"The effort's there, the boys crashed and bashed and there should be some players at our footy club that would be really proud of their performance tonight," Crows coach Brenton Sanderson said after the match.
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The Hawks seized early control with a dominant opening term, booting four goals before the Crows could reply, and led 5.2 to 1.4 at quarter-time.
Hawthorn extended their lead to 28 points in the opening minute of the second term but Adelaide's Dangerfield changed the tone of the match, hoisting his side back into the contest.
Dangerfield collected 20 disposals and kicked his two goals in the first half as the Crows edged within two points at half-time.
The Hawks surged in the third, with ex-Adelaide forward Jack Gunston booting two of three goals as the flag fancies created a 17-point buffer.
But just when Adelaide looked gone, late majors to Sam Jacobs and Richard Douglas helped the Crows sneak within five points of the Hawks at three quarter-time.
Star Crow Thompson goaled for a one-point lead early in the last, which stunned the Hawks into top gear as they booted four majors in an eight-minute burst to seal a win.
ADELAIDE 1.4 5.9 8.9 11.12 (78)
HAWTHORN 5.2 6.5 9.8 13.11 (89)
Adelaide: Jenkins, Dangerfield, Kerridge, Thompson 2, Douglas, Jacobs, Vince.
Hawthorn: Gunston 3, Hill, Breust 2, Hodge, Lewis, Puopolo, Smith, Osborne, Roughead
Adelaide: Dangerfield, Talia, Reilly, Sloane, Thompson, Vince
Hawthorn: Hodge, Mitchell, Lewis, Gibson, Breust, Smith
Adelaide: Matthew Wright replaced Jarryd Lyons in the third quarter.
Hawthorn: Jonathan Simpkin replaced Michael Osborne in the third quarter.
Umpires: Margetts, Chamberlain, Armstrong
Official crowd: 37,324 at AAMI Stadium