American Lance Armstrong did not start the stage, becoming the fourth prominent rider in four days to drop out.
Poli took off with 170 kilometers left in the stage from Montpellier to Carpentras, building up a more than 24-minute lead over the main pack that included Indurain.
The leaders were not concerned about Poli. He was more than one hour 22 minutes behind near the bottom of the overall standings.
As the pack approached Mont Ventoux, a 1,909-meter climb about 40 kilometers from the finish, Indurain took matters into his own hands. He took off with only a small group able to stay with him, cut the lead down to six minutes by the peak, then headed downhill at speeds close to 110 kilometers per hour.
Misjudging one curve, Indurain came within a meter of the edge of the mountain. He had to put his foot down to gain control of his bike.
Once back on the flats over the final 10 kilometers Poli was able to hang on, and won the stage by three minutes.
Second went to Alberto Elli of Italy just ahead of Pascal Lino of France.
Indurain was about four minutes behind Poli and did not lose any of his overall margin to Richard Virenque of France, still 7:56 behind in second place.
Armstrong added his name to a number of top riders who have dropped out recently in the race.
Last Friday it was Claudio Chiappucci, twice second in the last four years, bowing out with a virus.
Tony Rominger, runner-up last year, went out on Saturday, also a victim of an internal illness. Rominger had thought he was suffering from an intestinal virus since earlier last week and hoped to allow some time for recovery.
He never could get in the race. His Mapei teammates tried to lead him back when he was flagging, but Rominger finally spoke with his team director and got off his bike.
Two-time world champion Gianni Bugno stopped on Sunday, too tired to put up a decent fight.
Armstrong, who followed Bugno as world champion in 1993, dropped out Monday.
Last year Armstrong was the youngest to win an individual stage in the Tour but dropped out before the Alps to avoid getting burned out.
In Sunday's 14th stage, Rolf Sorensen won the 201-kilometer stretch from Castres to Montpellier.
Saturday, Bjarne Riis of Denmark, fifth in the Tour last year, won the 13th stage on a late breakaway. The route covered a fairly flat 223 kilometers after two tough stages in the Pyrenees.
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