The penalty, in lieu of a drive-through because it was awarded after the finish of the race, relegates the Scuderia Toro Rosso driver from 12th on the road to 16th in the final results.
The collision happened as Gutierrez made a move up the inside at the Turn 13 right-hander, which he appeared to have made stick before clashing with Vergne's Toro Rosso as they moved towards the exit of the corner.
The FIA stewards panel, including 1992 world champion Nigel Mansell, held Vergne responsible for the incident, even though Vergne said Gutierrez had hit him.
"On the last lap, I tried to pass my team-mate at Turn 1, and it didn't work and we ran wide, but I think he had used a bit of KERS on the straight so I couldn't pass him," said Vergne.
"I used all my KERS on the next straight to try and outbrake him but then Gutierrez clipped my rear wheel at Turn 12 and he tried to pass me and we touched."
Sauber head of trackside engineering Tom McCullough praised Gutierrez for the quality of his move and agreed the Mexican was not at fault.
"It was a cracking move and Vergne turned in on him," McCullough told AUTOSPORT.
"It looked like Esteban gave him enough room at the exit."
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