Fumic and Avancini raced home in a time of 4hr 25min 35sec over the 101km course to retain the overall lead and the yellow jersey.
Second over the line was Christoph Sauser and Jaroslav Kulhavy (Investec-Songo-Specialized), who crashed inside the final 5km, while third on the day went to Jochen Kaess and Markus Kauffmann (Centurion Vaude 1).
“That was very good, very very good. We had a great run. Our plan was to get to the front and stay there. That way we could control the pace,” Fumic said. “The plan worked very well for us today. Nino (Schurter) was pushing, Susi (Christophe Sauser) was pushing, but we were able to push harder.
"We were lucky with Jaro (Kulhavy) crashing, but that happens. It was hot out there, very hot, but we came out on top and are very pleased.”
Also happy with their day’s riding were the composed Investec-Songo-Specialized pair, with Kulhavy shrugging off the dust from the crash.
“The crash was unfortunate, but nothing serious," he said. "I'm very happy with our ride today, I feel it was a good performance. We are both enjoying the racing.”
Jennie Stenerhag and Esther Suss of the Meerendal CBC team sweated their way to a healthy overall lead and now have nearly a nine-minute advantage over Sabine Spitz and Robyn de Groot (Ascendis Health).
The Ascendis Health duo, who started the stage with a 39 second lead after winning the prologue, had a tough day with a mechanical giving their rivals an early advantage, and then just as they starting clawing their way back, Spitz fell down a crevice and cut her head badly.
The German former Olympic gold medallist arrived at the finish with blood on her face and went off to the medics for potential stitches to close the wound.
Mariske Strauss and Annie Last (Hansgrohe Cadence OMX Pro) finished third and are now 13 minutes off the lead, but the big tears were from Ariane Lüthi and Adelheid Morath (Spur), whose hopes of victory seem to have almost certainly disappeared.
The pre-race favourites are a massive 23-minutes behind Stenerhag and Suss and after two disappointing days in the saddle do not look to be able to mount any sort of a challenge against the top teams.
Stenerhag, who last year was forced to withdraw from the race with an elevated heart-rate, was cautiously optimistic.
“I was in the same position last year at this point so I am not going to be taking anything for granted,” she said. “I did not know how far ahead we were but we were in front so we could take it a bit more carefully and not take any risks.”
Suss was relieved to have survived a tough stage in intense heat that reached into the high 30s.
“It was really a tough day," Suss said. "Early on it was windy and it was hard to fight against the winds. In the beginning, I was not so fine, I had a high heart rate but after the Hansgrohe Women's Hotspot my rate was much better and we were able to race.
“Tomorrow we will do what we can do and must go fast as we can but not overturn (crash). We must not take too many risks on the downhills. You can lose more in the downhills if you crash or whatever than you can make up by going quickly.”
Stage 2 of the Absa Cape Epic starts at Hermanus High School and finishes at Elandskloof in Greyton. The stage is 102km long and has 2350 metres of climbing.