A shock looked to be on the cards when Goransson and Routliffe attacked Stefani's first service game, both contributing winners to break serve in just the third game, and the El Salvadorian/Brazilian duo failed to break back, as the rest of the set went with serve, giving the unseeded pair a 6-3 win.
But the favourites showed their potential in the second set, seldom dropping a point from serve before finally earning a break in game eight off the serving of the New Zealander, who had no answer to Stefani's forehand, before two-time French Open Men's Doubles champion Arevalo served successfully for the set in the next game, taking it 6-3.
That took the match to a 10-point tiebreak third set, in which a double fault from Arevalo put the Swedish-New Zealander pair in the ascendency, only to let their opponents off the hook at the next point, as Routliffe was forced into an error following her own serve.
The next five points went with serve, putting Goransson and Routliffe 5-4 up, before a crazy passage of play which saw the next five points go against serve, as the underdogs let a 7-4 lead close to 7-6, before going 8-6 clear.
Stefani and Arevalo finally won a point off serve to reduce the gap back to one, but two points well taken off the serving of the 32-year-old Swede got Goransson and Routliffe over the line, winning the match 6-3, 3-6, 10-7.
They will meet French wildcards Geoffrey Blancaneaux and Leolia Jeanjean in the Second Round.
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