They hit nine winners and won 73 per cent (35/48) of their first-service points on their way to victory, recovering from 2-5 down in the first set.
De Minaur, who in singles, is No. 15 in the FedEx ATP Rankings, also partnered Reid at Roland Garros earlier this month. The Australians advanced in 77 minutes and will next face top seeds Nikola Mektic and Mate Pavic.
The pair has enjoyed a sensational season, winning seven tour-level titles, with their latest victory coming at the Viking International Eastbourne last week. They are now 43-6 in their first year together.
Federer Sweeps Past Gasquet For Third-Round Berth
Due to rain at the All England Club on Monday and Tuesday, the first and second-round doubles matches will be contested over three sets, before returning to five from the third round.
Granollers and Zeballos won 90 per cent (27/30) of their first-service points to set up a meeting with British brothers, Ken Skupski and Neal Skupski. The Spanish-Argentine tandem clinched their third ATP Masters 1000 title at the Mutua Madrid Open (d. Mektic/Pavic) in May.
There was also success for eighth seeds Lukasz Kubot and Marcelo Melo, who fought past Nathaniel Lammons and Jackson Withrow 6-4, 5-7, 6-4. They hit 10 winners to advance in two hours and two minutes.