Roberto Firmino, Naby Keita and Rhian Brewster all netted for the Premier League champions in their opening pre-season friendly in Austria, where they have been training in preparation for the 2020-21 campaign.
There was also a Liverpool debut for Kostas Tsimikas, who was introduced at half-time as part of wholesale changes made by manager Jurgen Klopp.
The Greek left-back is a new arrival on Merseyside, having joined from Olympiacos in an £11.75million deal earlier in August.
Firmino struck after just 15 minutes against Stuttgart, who were promoted back to the Bundesliga last season after finishing as runners-up in the second tier of German football, behind Arminia Bielefeld.
The Brazilian then teed up Keita shortly after the half-time break, before England Under-21 international Brewster - who is attracting plenty of transfer interest after impressing on loan at Championship Swansea last term - wrapped up a straightforward win with just over 20 minutes remaining.
Liverpool were without Alex Oxlade-Chamberlain against Stuttgart, with the midfielder set to miss Liverpool's pre-season campaign as a result of a knee injury sustained in training earlier this week.
Next up for Liverpool is another Austrian friendly against RB Salzburg on Tuesday night, before they take on FA Cup winners Arsenal in the Community Shield at Wembley on August 29.
The Reds begin their top-flight title defence against newly-promoted Leeds United at Anfield on September 12 before the visit of Chelsea is followed by a league clash against Arsenal.