The Renault-owned team successfully argued there was a "significant and relevant new element", allowing the penalty to be overturned on review and double world champion Alonso restored to seventh place from 15th.
Stewards in Austin originally accepted last Sunday a Haas post-race protest about the safety of Alonso's car, which had been allowed to continue on track despite a flapping mirror that eventually fell off.
Alpine subsequently argued the Haas protest was inadmissible because the team submitted it 24 minutes too late.
A hearing on Thursday at the Mexican Grand Prix revealed Haas were told by race control they had an hour to lodge a protest, rather than the 30 minutes stated in the International Automobile Federation's (FIA) international sporting code (ISC).
Alpine then petitioned for a right of review, with sporting director Alan Permane saying his team were also unaware until 8.53 p.m. last Sunday that Haas had lodged their protest after the deadline.
Permane added it was not until Thursday that Alpine "became aware that an FIA official in race control had advised Haas that it had one hour to lodge its protest when the ISC prescribed 30 minutes".
The stewards accepted grounds for a review, which was held immediately.
Alpine stated that "an FIA official cannot give a competitor permission to contravene the ISC" while Haas said they would have submitted a handwritten protest within the deadline had they not been told they had an hour to do so.
Stewards ruled the original Haas protest inadmissible because it had not been "impossible" for the team to meet the deadline.
Alpine, in a battle for fourth place with McLaren, welcomed the return of six points.
Alonso had said he expected his demotion to be overturned and warned the sport otherwise risked creating a "huge problem".
