Breschel, who had not posted a victory since the Tour of Denmark in 2010, crossed the line at the end of the 159km stage between Santo Domingo De Silos and Lerma ahead of Nacer Bouhanni (FDJ-BigMat) and Ben Swift (Sky Procycling).
“We knew that the odds were good for Matti on this course,” Rabobank team director Erik Dekker said. “The run up in the last few hundred metres was difficult. It was harder than the race book made it look. There was talk of a two per cent slope, but as we found out for ourselves this morning, it was a steep six per cent.
“Matti said he was ready. We knew exactly what was coming and he kept good control. The last corner was not a 90-degree bend, so Matti could be led through and then it was actually easy.
"It’s a beautiful victory, his first with us and his first in two years. He yearned to do well here and he regretted that on Wednesday and yesterday we were not successful. But now the spell is broken. Saturday is a similar stage and we will go all out for him.”
Katusha's Moreno, who won the first two stages, hung on to the leader's jersey.
Stage three results (top 10):
1. Matti Breschel (Rabobank) 3h52’35”
2. Nacer Bouhanni (FDJ-BigMat)
3. Ben Swift (Sky Procycling)
4. Allan Davis (Orica-GreenEdge)
5. Daniele Ratto (Liquigas-Cannondale)
6. Jon Aberasturi (Orbea)
7. Yukihiro Doi (Argos-Shimano)
8. Jérémie Galland (Saur-Sojasun)
10. Stefano Garzelli (Acqua & Sapone)