In the end, centre Ash Handley’s second try of an entertaining West Yorkshire derby after 76 minutes and Kallum Watkins third goal rescued a point for the visitors.
Winger Jared Simpson grabbed two first-half tries on his first appearance of the year while Danny Brough kicked five goals from five attempts as Giants led 12-0, 14-6 and 20-16.
Thorman’s first selection since replacing Australian boss Rick Stone included debuts for teenagers Louis Senior and Sam Hewitt, while ex-Giant Brett Ferres returned to the Leeds side for the first time since last season’s Grand Final.
Simpson had not featured in Super League since last September’s 36-12 home defeat by the Headingley outfit.
Huddersfield made the perfect start to the post-Stone age with Simpson squeezing in at the corner after only 90 seconds. Brough nailed a superb touchline conversion to leave the visitors trailing 6-0.
Leeds should have registered their own first points after eight minutes, only for Richie Myler to drop the ball with an unguarded try line in front of him,
Hewitt, 19, only had to wait nine minutes to join Senior on debut, a blood-bin replacement for Aaron Murphy.
Simpson, back from a four-game dual-registration spell at Dewsbury, struck again after 17 minutes with Brough again booting the extras.
It proved a wake-up call for the Rhinos as Watkins crashed over after 22 minutes and duly converted his own try to cut his team’s deficit in half.
The Giants, though, were good value for a 14-6 interval lead, failing to turn attacking sets into more tries but with Brough kicking a 39th-minute penalty for Mikolaj Oledzki’s high tackle on Simpson.
But within 12 minutes of the restart Leeds struck back as Giants conceded two tries initiated by penalties for holding-down offences on Ryan Hall and Tom Briscoe.
Hall had his revenge by going over after 44 minutes while Handley, with the assist for the England winger’s touch down, dummied his way over eight minutes later. Watkins converted Handley’s individual effort and Leeds led 16-14
Given Giants’ spirited performance it never looked certain to be a winning advantage. Hooker Adam O’Brien duly restored Huddersfield’s lead after 64 minutes, burrowing over from dummy half for Brough to add a fourth goal.
His fifth came via a 73rd-minute penalty, leaving Leeds needing to score twice to win the game.
Handley, though, came to the rescue with his second try four minutes from time with Watkins’ fourth goal tying the scores.
There was still time for Rankin to go for glory but it was not to be.