Katusha rider Isaichev got the better of Euskaltel's Ruben Perez and Team Sky's Salvatore Puccio respectively as the 193km ride from Trimbach to Gansingen reached a thrilling climax.
It was the Russian's first tour win at the age of 26. He has been a professional since 2005.
"I'm so happy about this victory," he said. "it's the first one of my professional career, and it came in such an important competition such as 'Tour de Suisse'.
"Moreover, the way it came was extraordinary. I felt in a great shape during the whole stage, and my motivations were high because I knew that, in a sprint against the riders which were in the breakaway with me, I was the favourite.
"And, in fact, I managed to win quite easily. Really, it was a great day for me. I've always imagined my first victory in pro races, but I would have never thought of such a great win."
Saxo Bank's Karsten Kroon and Sebastien Minard of AG2R just missed out on the podium, with Italy's Liquigas rider Daniel Oss five seconds back in sixth place having gone too early with 500 metres remaining.
That group of six - plus Klaas Lodewyck, who faded 1:50 off the pace and finished back in seventh after winning one of the intermediate sprints - had broken away from the peloton around 34km into the stage, with all seven trading sprint wins before the final climb at Buerersteig.
Minard initially attacked with 2km remaining, but he was reined in by Perez and Oss, with Isaichev - who had won the climbers' jersey by this point - surging in the final metres to claim the stage victory, with Puccio overhauling Oss for third.
Rui Costa finished in the main peloton around 11 minutes back and sits almost 21 minutes ahead of Frank Schleck in second and Roman Kreuziger in third.
Thursday's stage six is a relatively flat 198.5km ride between Wittnau and Bischofszell.