Bradford were trailing by 16 points when the Great Britain forward went off. Without him, they exploded into life, scoring six tries to win the match.
Their outstanding player, Paul Johnson, set the ball rolling when his side ran the ball on the last tackle of a set of six and Lesley Vainikolo went over from Andy Lynch's offload.
Huddersfield were conceding too many penalties and paid the price when Stuart Fielden's try put Bradford back in front.
From that point, the Bulls ran away with it, with further tries from Vainikolo, Brad Meyers and Lee Radford, but it had been a very different story in the first hour.
Huddersfield were by far the better side in the early stages and deserved their 12-point lead.
Stanley Gene's perfect pass and Chris Nero's break set up Marcus St Hilaire for their first try and Brad Drew's clever kick gave James Evans the second.
The prop Joe Vagana did most to bring Bradford back into the game. He got the ball to Ian Henderson for their first try and his next run set up the position from which Robbie Paul and Michael Withers released Johnson for the equaliser.
When Paul Deacon scored from Lynch's pass it seemed that the Bulls were warming to their task, but the Giants were in a determined mood, nobody more than Gene. He collected a lovely offload from Eorl Crabtree for the try that levelled the scores and then put Huddersfield back in front by breaking through to lay one on for Paul March.
Huddersfield looked to be on their way to victory with brilliant tries from Crabtree and Lee Greenwood after the break, but Bradford's resurgence saw them home. The good news for them is that there will be much more to come from Morley who admitted: "I felt off the pace, but I will be a lot better next week."
Bradford: Withers; Pryce, B Harris, Hape, Vainikolo; I Harris, Deacon; Peacock, Henderson, Fielden, Johnson, Meyers, Radford. Substitutes used: Vagana, Paul, Lynch, Morley.
Huddersfield: St Hilaire; O'Hare, Evans, De Vere, Greenwood; Thorman, Gene; Jackson, Drew, Gannon, Nero, Jones, Crabtree. Substitutes used: March, Smith, Grayshon, McDonald.
Referee: K Kirkpatrick (Warrington).
* Hull got their Super League campaign back on track with a 32-30 away win over Wakefield yesterday. The victory, Hull's fourth against the Wildcats this season, makes next Friday's meeting with Warrington at the KC Stadium a direct shoot-out for fourth place in the table.Reuse content