The game was interrupted twice because of flares in the first half and the home fans also invaded the pitch in the closing stages as Memphis Depay, Nabil Fekir, with a double, Mariano Diaz and Bertrand Traore all got on the scoresheet.
St Etienne played almost half of Sunday's game with 10 men after Leo Lacroix was sent off for a dangerous tackle on Fekir two minutes into the second half.
The win put Lyon on 25 points from 12 games, seven adrift of leaders Paris St Germain, who themselves won 5-0 at Angers, and three points off second-placed AS Monaco who went one better by beating visitors En Avant Guingamp 6-0 also on Saturday.
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It was Lyon's biggest league victory at the Geoffroy Guichard stadium in France's fiercest derby.
Olympique de Marseille are fourth on 24 points after a 5-0 thrashing of Caen earlier on Sunday.
FLARES INTERRUPTION
The match was interrupted for almost 10 minutes because of flares early in the first half, with Dutch international Depay opening the scoring after 10 minutes with a clinical finish after being set up by Houssem Aouar.
Six minutes later, St Etienne lost key midfielder Romain Hamouma through injury.
In the 25th, Fekir unleashed a fierce left-foot shot past Stephane Ruffier from 20 metres to extend the lead.
Lacroix was shown a straight red card early in the second half for a rough tackle on Fekir ending St Etienne's hopes of making a comeback.
Diaz poked the ball home from close range to put Lyon 3-0 up in the 58th minute before setting up Traore for the fourth as Les Verbs began to fall apart, with Fekir adding a fifth in the closing stages to rub salt into the home side's wounds.
Fekir took off his shirt to show it to the home fans and some of them invaded the pitch in reaction.
"It's a pity. It is useless to provoke. We should remain humble," Lyon coach Bruno Genesis said of Fekir's gesture.
The game was interrupted for half an hour and resumed in front of almost empty stands.
Nice striker Mario Balotelli went from hero to villain in a 1-0 win at home Dijon as he converted a penalty before the break but was sent off a minute from time for a dangerous tackle.
The win took Nice to 15th on 13 points, a point above Dijon.
(Reporting by Julien Pretot; Editing by Ken Ferris)
