Hamilton worked his way through the field from 14th on the grid and found himself up to fifth by the end of the 15th lap.
"Highly unlikely but you've got to believe" Hamilton said of his chances of winning from his starting spot of 14th.
"I kept pushing, kept believing and I manifested my dream today, so thanks to God".
Bottas accepted his team's decision to force him to hold behind Hamilton late in the race.
"When Seb went off I thought now was a good time, but I think the safety car came at a better time for Lewis," Bottas said.