11th seeds Paes and Nestor quelled the challenge from the Serbian pair of Victor Troicki and Dusan Lajovic 6-3 6-4 7-5 after battling hard for an hour and 42 minutes on Court Number six at the SW 19.
Purav Raja, who had qualified with Martin, fought their hearts out before losing 1-6 4-6 6-4 6-7 (7-9) against the 2012 Wimbledon champions Jonathan Marray and Frederik Nielson.
They broke rivals at love in the sixth game for a 4-2 lead and then the two pairs held serve with Paes and Nestor pocketing the opening set.
The second was more tight with scoreline 3-3 after initial battle. Paes and Nestor broke in the seventh game. The lead stayed with the 11th seeds as they served out the set in the 10th to take a firm grip over the match.
The third set was another close battle as they pairs served strong for a 5-5 scoreline. Paes and Nestor broke finally succeeded in getting that crucial break in the 11th game and then saved two break chances while serving for the match and closed it in their favour when the rivals committed a backhand error.