The stage was won by former world champion Luc Leblanc of France, who made his move with eight kms remaining in the punishing climb to the ski resort of Les Arcs. Veteran Swiss Tony Rominger was second place 47 seconds back and young Austrian Peter Luttenberge third a further five seconds behind.
Berzin ended the stage in 11th place, four seconds after Luttenberger, to take the overall lead from Frenchman Stephane Heulot, who retired with 37 kms remaining.
Heulot, who took the race lead after Wednesday's fourth stage, got off his bike in the Cormet de Roselend pass, the second of the day's three climbs. He restarted and rode for a few hundred metres but then pulled out of the race and got into a team car.
In the overall standings, Berzin now has a slender lead of less than a second over world champion Abraham Olano of Spain, who ended the stage in sixth place in the same group as the Russian. The two will battle it out with Rominger, third overall and seven seconds back, over Sunday's uphill, 30.5-km time-trial from Bourg-Saint-Maurice to Val d'Isere.
``I don't know if I can win the Tour,'' said the 26-year-old Berzin. ``It's a long, tough race and you never know what can happen.''
Five times Tour winner Indurain looked almost effortless in the Madeleine pass, reaching the summit in second place behind Frenchman Richard Virenque. The Spaniard was equally impressive in the Cormet de Roselend, coolly letting German Udo Bolts try his luck.
But in the final climb to Les Arcs, the Spaniard experienced one of his worst moments on the Tour, an event in which he has often been in a class of his own since his first win in 1991. Indurain was in a small group chasing Leblanc when he suddenly became unable to follow the pace. He lost considerable ground, accepted a feeding bottle, which could cost him a penalty, and eventually crossed the line in 16th position, four minutes and 19 seconds behind Leblanc.
``I don't know what was wrong with him, probably hunger pangs,'' said Leblanc. ``He's only human and even great champions have off-days. I'm sure he will recover.''
The win came as a relief for Leblanc, who has been through hard times since winning the road race of the 1994 world championships. ``I've been unlucky since the Tour started and I was looking for a revenge,'' said the Frenchman, who fell several times in the previous days.
Saturday's stage, on narrow, twisting roads made slippery by rain, was marred by more spectacular crashes including one by Belgian Johan Bruyneel. He missed a curve in the descent from the Cormet de Roselend and was thrown over over a low wall, a hair's breadth from a ravine, but escaped with superficial bruises.
``I'm happy to be alive,'' said Bruyneel. ``I thought I was dead. It was like I was flying. I fell into a tree. I still don't know where my bike is.''
Indurain was not the only one to suffer as world number one Laurent Jalabert of France, regarded as one of the few men capable of depriving him of a record sixth Tour win, struggled all day and lost some 12 minutes.
The Frenchman, who took the yellow jersey after Wednesday's fourth stage, restarted soon stopped again and got into a team car.
Boardman, trying to go the full distance for the first time in the world's greatest cycle race, came 47th of the seventh stage in the Alps nearly 29 minutes behind Luc Leblanc of France. He later realised that somebody had entered his hotel room and stolen his wallet and his watch.
``It was my worst day in a cycle race,'' said the pursuit Olympic champion, now 41st overall 33 minutes and 18 seconds behind leader Yevgeny Berzin of Russia. ``In the first pass, I was okay,'' he said. ``I was in the second group and I was able to come back. But then I had hunger pangs and I had to stay with Prudencio Idurain, Miguel's brother, to finish the stage.''
Boardman, who retired in the 11th stage for his first Tour participation in 1994 and crashed out of last year's race by falling in the prologue, said he had little to expect now.
``Stephane (joint overnight leader and team mate Heulot) is out of the race and we will have to change our tactics,'' he said. ``For me, it's all over. That's the Tour de France. I'll try to reach Paris.''
France's Luc Leblanc (Polti) took off in the stage's last terrible climb, rejoined Laurent Dufaux (Festina) with two kilometers left in the stage and resisted Tony Rominger (Mapei) - now third in the overall standings - and Peter Luttemberger (Carrera). Dufaux had bridged the gap with Udo Bolts (Telekom) 10 kilometers before the finish. Bolts had broken away just before the Cormet de Roselend (km 163) with Patrick Jonker and Alberto Elli.
Two of the race's favorites, Jalabert (Once) and five-time winner Indurain (Banesto), had serious problems today. For the first time in six years, a dehydrated Indurain couldn't stay with the pack and lost over four minutes in the stage's last climb, finishing three minutes and thirty-two seconds behind the overall lead. Fourth yesterday, Jalabert had lost touch with the field earlier, in the first climb, the Col de la Madeleine, because of Bjarne Riis's Telekom teammates' hard work up front.
Alex Zulle also had a tough time, falling twice but managing to come back up to the lead group. He fared only slightly better than Indurain in the last climb and finished two minutes and thirty seconds behind the overall lead.
Evgueni Berzin (Gewiss) took the yellow jersey for tenths of seconds by staying close to the lead. World champion Abraham Olano (Mapei) is .16 seconds behind in the overall standings.
Stephane Heulot had quit earlier, in the middle of the stage's second climb, the Col du M=E9raillet. He had stopped twice, weeping, his knee hurting, and tried to continue, but to no avail.
This first stage in the Alps also saw Richard Virenque (Festina) recapture the best climber jersey and finish sixth in the overall standings. Virenque was the Tour's best climber in 1994 and 1995.
Yesterday's best climber, Leon Van Bon, withdrew.
The decimated Gan team's Frederic Moncassin kept the best sprinter jersey. Yesterday Seigneur gave up and Moreau was eliminated, and today Heulot withdrew while former world champion Chris Boardman was finishing 28 minutes behind the overall lead.
After the rainy and windy first six stages, which took their toll on the riders, the climbs were too much for the pack, with seven withdrawals in all, three in the Brescialat team alone. The riders should really appreciate tomorrow's time trial.