The stewards examined slow motion footage of Vettel's actions from the moment that he had regained control and started steering his car - and felt the evidence showed that he could have made different choices that would have been within the rules.
The footage clearly captures Vettel correcting an oversteer moment as he rejoins the track - which is shown by a sharp steering wheel movement to the right.
Shortly after that, Vettel has sorted the oversteer and begins steering to the left to follow the direction of the circuit - suggesting he is now under control.
But a split moment later, rather than keeping to the left, Vettel is shown to release the steering wheel - which allows his car to drift to the right, cutting off the route that Hamilton would have taken had he had clear space.
The movement to straighten the wheel, which put the Ferrari into the path of Hamilton's Mercedes, is believed to be key to the unanimous decision by the stewards to punish Vettel.
The stewards also used an extra CCTV camera view of the incident, which was not broadcast on the international television feed, showing Vettel moving his head and looking in the mirrors to see Hamilton was during the moments when he was releasing the wheel to the right.
Precedent for the decision to punish Vettel for both rejoining the track in an unsafe manner and forcing a rival off the track was made last year in Japan when Max Verstappen was hit with a five-second penalty for a collision with Kimi Raikkonen at the chicane.