Second-seed Errani came into the WTA International clay-court event on a high after completing a career grand slam by winning Wimbledon with women's doubles partner Roberta Vinci last week.
However, the Italian fell short of what would have been a 17th WTA Tour final after going down in straight sets to the 21-year-old on Saturday.
Rogers made a superb start by breaking Errani in the very first game, although she gave up the initiative as Errani hit back in game six.
The remainder of the set went on serve before an epic tie-break ensued.
After saving two set points, Rogers squandered two of her own - only to eventually clinch the tie-breaker 14-12.
This time it was Errani's turn to record an early break in the second set, although Rogers was able to level, winning 75 per cent of the points on her first serve before moving 5-3 ahead with another break.
The American showed no sign of nerves in serving out, holding to love to seal victory and advance to the final.
There she will face fourth seed Andrea Petkovic, who came from a set down to defeat Grace Min 4-6 6-2 6-4.
Ranked 138 in the world, Min moved in front with a third break of the first set in game 10 before Petkovic hit her stride in the second to level the match.
The third set was much more even, Petkovic wasting two match points before eventually securing victory and progressing to her ninth WTA Tour final.