Tuchel's six straight competitive wins since taking charge broke Carlo Ancelotti's club record from 2011 , with Julian Draxler taking his chance to impress in the absence of rested Neymar and suspended Mbappe.
Edinson Cavani, Angel Di Maria and teenage substitute Moussa Diaby were also on target in a comfortable victory for the champions.
PSG were able to ease to victory in the second half, retaining energy for Tuesday's trip to Anfield in their Group C opener against last season's beaten Champions League finalists.
Marco Verratti made his first competitive appearance since March after recovering from a groin injury but Tuchel indicated he may make a late call over one of his players.
"I know 10," Tuchel said to Canal+ Sport when asked about his selection plans for the trip to Anfield.
"Not yet the 11th and I do not know my game system."
PSG made a slow start at the Parc des Princes but, after Draxler's clever header got them up and running, the champions eased to victory.
"The team have proven their hunger for wins and I am very happy for that," Tuchel added.
"We played with seriousness and intensity. The second half was top."
wins in matches. Next stop... Anfield! pic.twitter.com/tDOzjhzWw2— Paris Saint-Germain (@PSG_English) September 14, 2018
Saint-Etienne missed a string of early chances and their coach Jean-Louis Gasset felt a four-goal defeat was a harsh result.
"I said before the game that we would have to be at 110 per cent to get a result in Paris," he told reporters.
"There was something to be done, of course. The game plan was to play low and counter in the first half. It was done to perfection. Unfortunately, we did not manage to score.
"We knew PSG were stronger than us but four goals are expensive. This is our first defeat of the season, we will work to prepare the next matches, try to take points."