New Zealand drivers Earl Bamber and Brendon Hartley, alongside Porsche team-mate, German Timo Bernhard finished second at the opening round of the FIA World Endurance Championship.
Hartley came out of the pits with an eight-second lead over the Toyota, but Buemi was able to close him down and get past to take the lead eight laps before the finish of the six-hour race.
The scans were undertaken because the accident at Copse in the fourth hour of the race triggered the so-called "medical light" in the vehicle. Tandy recovered to finish 47 seconds off race victor Buemi, whilst the sister vehicle continued to push and saved time during a full course yellow period. Mucke was now leading LMGTE-Pro while Alessandro Pier moved to second in the #51 AF Corse Ferrari 488 GTE.
"I'm really happy. It's an fantastic feeling", Buemi said to the WEC's Louise Beckett in parc ferme. "It was a little bit a combination of the anti-roll bar, the wet and I touched the curb with my rear tire".
Hartley and Bernhard were in the 2015 championship-winning Porsche, along with Australian Mark Webber. The second Porsche faded to a distant third, 46s behind the winners in the final stages. A lengthy safety vehicle period followed while the badly damaged Toyota was extracted from the track. The No. 7 vehicle shared by Mike Conway, Kamui Kobayashi and Jose Maria Lopez was a match for the race-winning auto until the rear anti-roll bar broke shortly before the end of Conway's opening double stint.
The auto underwent repairs and returned to the race to finish in 23rd position, which gained it fourth-place manufacturer points in LMP1.
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The reigning European Le Mans Series champion pitted with 20 minutes on the clock for a front-left tire, briefly losing the lead, but Fred Makowiecki followed suit soon after, putting the Ford back ahead of the Porsche 911 RSR.
In the end Toyota Gazoo Racing pulled off a thrilling last-gasp victory.
That appeared to have put them out of contention, but the safety vehicle gave them the break they need and undermined the chances of the sister auto shared by Stefan Mucke, Billy Johnson and Olivier Pla, which had looked on course for victory.
In LMP2, Jota-run #38 Jackie Chan DC Racing ORECA-Gibson of Oliver Jarvis, Thomas Laurent and Ho-Pin Tung claimed an easy win, which saw the British driver victorious on LMP2 debut having seen Audi exit the series a year ago. They were another crew to benefit from the safety vehicle, before which they had trailed the Signatech Alpine ORECA driven by Nicolas Lapierre, Gustavo Menezes and Matt Rao by a clear margin.
This allowed the Irishman to come through to take the win in the Clearwater Ferrari 488 GTE alongside co-drivers Keita Sawa and Mok Weng Sun.
Matt Griffin took the GTE-Am class win on the last lap as Pedro Lamy and Miguel Molina, fighting for the lead in the No. 98 Aston Martin Vantage GTE and Spirit of Race Ferrari, collided at Stowe.