The winning Audi R18 e-tron quattro passed the second-place car for the lead with just over five minutes of the race remaining on a day that the two Joest-run cars battled hard throughout the six hours.
Both cars had spent time in the lead over the first third of the race and Andre Lotterer, who shared the second Audi with Benoit Treluyer and Marcel Fassler, was able to build a gap of more than a dozen seconds over Kristensen.
A front driveshaft failed on the Lotterer car over the second half of his stint, robbing the Audi of the power from its energy-retrieval system over the remainder of the race.
McNish caught and passed Treluyer after they took over their respective R18s for the run to the flag, only for the Frenchman to jump back ahead when he was short-fuelled at the next round of pitstops.
McNish then spun avoiding an Aston Martin just as Treluyer made his final stop. He flat-spotted his tyres, leaving the team with no choice but to change all four Michelins.
That left him just under 30 seconds behind his team-mate, but on fresh rubber he was able to close down on Treluyer and pass him at Brooklands four laps before the finish.
McNish, who crossed the line just over three seconds ahead, said: "It was nip and tuck with our sister car all the way through and we always knew it was going to be decided by seconds and nothing more. There are no team orders at Audi, there is no question about that.
"The last stint was one of the hardest, especially at the end of a six-hour race."
Toyota was never in the game at Silverstone, at which it ran two of last year's TS030 HYBRIDs against the 2013-spec Audis.
Anthony Davidson, Stephane Sarrazin and Sebastien Buemi ended up taking the final place on the podium for the Japanese manufacturer, one lap down on the Audis.
The second Toyota, shared by Alex Wurz and Nicolas Lapierre, was a further minute behind after the latter driver made an unsuccessful decision to gamble on intermediate tyres during a short-lived rain shower.
The Anglo-Swiss Rebellion Racing LMP1 privateer squad took fifth and sixth positions with its pair of Lola-Toyota B12/60s, Neel Jani, Nick Heidfeld and Nicolas Prost beating home Andrea Belicchi, Mathias Beche and Congfu 'Frankie' Cheng.
Honours in the LMP2 category went to the G-Drive/Delta-ADR squad. Antonio Pizzonia, Tor Graves and James Walker came out on top in a battle with best of the OAK Racing Morgan-Nissan LMP2s shared by Olivier Pla, Alex Brundle and David Heinemeier Hansson.
Aston Martin Racing dominated the GTE classes: Stefan Mucke, Darren Turner and Bruno Senna claimed victory in the Pro category and Allan Simonsen, Christoffer Nygaard and Kristian Poulsen in the Am division.
1. P1 Kristensen/Duval/Mcnish Audi 197 laps
2. P1 Lotterer/Treluyer/Fassler Audi + 3.462s
3. P1 Davidson/Buemi/Sarrazin Toyota + 1 lap
4. P1 Wurz/Lapierre Toyota + 1 lap
5. P1 Prost/Jani/Heidfeld Rebellion Lola-Toyota + 4 laps
6. P1 Belicchi/Beche/Cheng Rebellion Lola-Toyota + 7 laps
7. P2 Graves/Pizzonia/Walker Delta-ADR ORECA-Nissan + 13 laps
8. P2 Pla/Heinemeier Hansson/Brundle OAK Morgan-Nissan + 14 laps
9. P2 Dyson/Marsal/Kimber-Smith Greaves Zytek-Nissan + 18 laps
10. P2 Perez Companc/Minassian/Kaffer Pecom ORECA-Nissan + 18 laps
11. P2 Baguette/Gonzalez/Plowmann OAK Morgan-Nissan + 18 laps
12. P2 Imperatori/Howson/Ka To KCMG Morgan-Nissan + 18 laps
13. P2 Rusinov/Martin/Conway Delta-ADR ORECA-Nissan + 21 laps
14. GTE P Turner/Mucke/Senna Aston Martin + 26 laps
15. GTE P Kobayashi/Vilander AF Ferrari + 27 laps
16. GTE P Dalla Lana/Makowiecki/Lamy Aston Martin + 27 laps
17. GTE P Lieb/Lietz/Dumas Manthey Porsche + 27 laps
18. GTE P Bruni/Fisichella AF Ferrari + 27 laps
19. GTE A Nygaard/Poulsen/Simonsen Aston Martin + 28 laps
20. GTE P Bergmeister/Pilet/Bernhard Manthey Porsche + 29 laps
21. GTE A Bornhauser/Canal/Rees Larbre Corvette + 31 laps
22. GTE A Potolicchio/Aguas/Peter 8Star Ferrari + 32 laps
23. GTE A Goethe/Hall/Campbell-Walter Aston Martin + 32 laps
24. GTE A Ried/Roda/Ruberti Proton Porsche + 32 laps
25. GTE A Krohn/Jonsson/Mediani Krohn Ferrari + 33 laps
26. GTE A Narac/Bourret/Vernay IMSA Porsche + 34 laps
27. P2 Nicolet/Merlin OAK Morgan-Nissan + 43 laps
28. GTE A Gerber/Griffin/Cioci AF Ferrari + 58 laps
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