Paire, ranked 25th in the world, had little trouble getting past British qualifier Jamie Baker 7-5, 6-2 in advancing on the grass courts of The Queen's Club in London.
Dimitrov, meanwhile, rallied from a set down to post a 4-6, 6-2, 7-6 (7-4) victory over Israeli Dudi Sela. His next opponent will be four-time champion and former World No. 1 Lleyton Hewitt, who got past American Michael Russell 4-6, 6-1, 6-3 in the Wimbledon tuneup.
Belgian Xavier Malisse also moved into the second round with a 6-4, 5-7, 6-4 win over Spaniard Guillermo Garcia-Lopez. He now goes on to face third-seeded former U.S. Open champ Juan Martin del Potro.
American Denis Kudla also logged a victory Monday, besting Argentine Federico Delbonis 6-0, 6-3.