The hosts cruised to victory in front of 14,473 spectators at the Swissporarena in Lucerne in their first home match since November, after three games on the road for the team ranked 19th in the world.
Switzerland coach Murat Yakin, who names his squad for the competition on Friday, was joined by Swiss Olympic giant slalom ski champion Marco Odermatt as they stood for the national anthems.
Steven Zuber opened the scoring in the 20th minute, lashing the ball into the top corner from the edge of the penalty box.
It was the AEK Athens winger's first goal for the national side since 2021.
Burnley forward Zeki Amdouni struck in the 47th minute with a shot across Estonia goalkeeper Matvei Igonen, set up in the penalty box by fellow half-time substitute Ruben Vargas.
Defender Nico Elvedi scored the third in the 63rd minute as Estonia failed to clear their lines from a Xherdan Shaqiri free kick.
Six minutes later, Chicago Fire midfielder Shaqiri, winning his 122nd cap, scored a penalty on the second attempt after the first effort was saved by Igonen -- although the goalkeeper was off his line, meaning the kick was retaken.
Switzerland host Austria at the Kybunpark in St Gallen, near the Austrian border, in a final warm-up on Saturday.
Austria are in Euro 2024 Group D, along with Poland, France and the Netherlands.
In the European Championship, Switzerland play Hungary on June 15, Scotland on June 19 and then hosts Germany on June 23 in Group A.
Switzerland reached the quarter-finals in the 2020 European Championship, their best-ever performance in the tournament.
