The 12th seeds reached the Second Round after a win in two sets over Frenchmen Giovanni Mpetshi Perricard and Alexandre Muller on Thursday.
However, Goransson's run in the mixed doubles alongside Irina Khromacheva ended at the first hurdle yesterday, via a straight sets defeat to Luisa Stefani of Brazil and Maximo Gonzalez of Argentina.
His week with Verbeek was not going to get any easier - the two were under pressure from the off this afternoon, as their opponents forced deuce in their first service game, before the Swede and Dutchman survived two break points before winning their second.
It seemed inevitable that Borges and Rinderknech would break through, and sure enough, in game six of the first set, Goransson's serve was broken and the unseeded duo took a 4-2 lead.
The next three games all went with serve with next to no incident, enabling Borges and Rinderknech to take a 6-3 victory in the first set.
Ranked 101st and 124th, respectively, in doubles, Borges and Rinderknech are both inside the top 75 in singles, and they continued to show their quality early in the second set by forcing a break in serve in the first game.
Goransson and Verbeek saved three break points off the Dutchman's serve, but a fourth was one too many and they fell behind again.
The next five games all went with serve, before a mammoth game seven saw Goransson and Verbeek save six break points off the serving of the 31-year-old Swede, before their opponents dealt them a blow by finally taking advantage on the seventh break point to go 5-2 ahead.
Desparate to cling on, Goransson and Verbeek saved the first match point in the next game, but could do nothing about the second, falling to a 6-3, 6-2 loss in straight sets.
Borges and Rinderknech will now face British pair Joe Salisbury and Neal Skupski in the Third Round.
