Tandy propelled the best of the German team's Porsche 911 GT3 Rs to the front after taking over from Bamber early in the 21st hour of double-points round of the GT World Challenge Europe Endurance Cup.
Tandy was fifth after the race went green with two and half hours to go at the start of the charge that took the Rowe car through to victory.
He moved past the AF Corse Ferrari 488 GT3 Evo of Alessandro Pier Guidi after being given a new set of Pirelli wet tyres in the worsening conditions at the start of the 23rd hour.
Tandy then jumped the Attempto Audi R8 LMS of Patric Niederhauser for second in the pits when they both stopped under full course yellows at the end of the hour.
The Rowe car then moved into the lead with just over an hour to go when the Sainteloc Audi team lost out when it pitted Dorian Boccolacci under the safety car that followed the FCY.
Tandy twice had to get the jump on Niederhauser, who shared the factory Attempto Audi with Frederic Vervisch and Mattia Drudi, at safety car restarts during the final hour.
The Rowe Porsche crossed the line four seconds ahead of Niederhauser despite a transmission problem that reared its head on the penultimate lap.
"I don't know what's happened, but we've split the diff, broken the gearbox or a driveshaft has popped out - there's oil coming out the back of the car," said Tandy, who now has outright victories in the Le Mans, Nurburgring and Spa 24-hour sportscar classics.
"With one and a half laps to go there was a horrendous noise. That is the most emotional last stint I've ever done."
The Dinamic Motorsport Porsche took the final podium spot after a dramatic move by Matteo Cairoli on Pier Guidi down the hill in Eau Rouge with just over 10 minutes to go.
The Italian team's Porsche 911 GT3 R co-driven by Sven Muller and Christian Engelhart had made dramatic progress up the leaderboard over the final 90 minutes to seal third place 24s in arrears of the Attempto Audi.
Pier Guidi, who shared the AF Corse Ferrari with James Calado and Nicklas Nielsen, dropped to fifth behind the best of the GPX Racing Porsches driven by Patrick Pilet, Matt Campbell and Mathieu Jaminet before the finish.
The Sainteloc Audi that Boccolacci drove together with Markus Winkelhock and Christopher Haase ended up down in sixth.
Top Mercedes-AMG GT3 was the Haupt Racing Team entry driven by Maro Engel, Luca Stolz and Vincent Abril in seventh. Its challenge for victory was thwarted by a penalty in the closing stages for causing a collision.
The Frikadelli Porsche of Frederic Makowiecki, Jorg Bergmeister and Dennis Olsen took eighth position.
Honda and Bentley filled out the top 10, the JAS run NSX GT3 of Renger van der Zande, Dane Cameron and Mario Farnbacher heading home the K-PAX Continental GT3 of Jules Gounon, Maxime Soulet and Jordan Pepper.
Pro-am honours were taken by the Barwell Lamborghini squad with the Huracan GT3 Evo driven by father and son Rob and Ricky Collard, Sandy Mitchell and Leo Machitski.