Bertogliati, a rider for the Lampre Daikin team, shocked the pack by starting a solo sprint for the line with just over a half-mile left in the 121.17-mile stage.
The 23-year-old recorded his first career stage win at the world's most famous cycling race and will wear the yellow jersey as the overall leader during Monday's second stage from Luxembourg to Sarrebruck, Germany.
Armstrong, the three-time defending Tour champion and winner of Saturday's prologue, is just three seconds off the overall pace in third place and remains the strong favorite to win the event again.
The Texan is looking to stay within striking distance of the leaders until the mountain stages begin until the 10th leg on July 17. Armstrong effectively won the 2001 title with his climbing prowess.
This year, Armstrong is attempting to join Frenchmen Jacques Anquetil and Bernard Hinault, Belgian Eddie Merckx and Spaniard Miguel Indurain as the only cyclists to have won the great race more than three times.
Laurent Jalabert, perhaps France's best hope for a Tour winner, is second overall. Raimondas Rumsas of Lithuania sits in fourth and Santiago Botero rounds out the top five.
Germany's Eric Zabel, the Telekom team's top rider with the absence of Armstrong's great rival, Jan Ullrich, finished second in Sunday's stage and took over the green jersey as the Tour's best sprinter. Zabel is gunning to win the green jersey for an unprecedented seventh time.