Center back Eric Bailly gave United the lead on the stroke of halftime with a close-range strike at a corner, and the visitors were comfortable in the second half before running amok in the final 10 minutes.
Eight goals scored and two clean sheets makes for an encouraging start to the season for Mourinho, who has built an imposing and clinical team that looks equipped to challenge for the title.
The Welsh team, which sold its star player Gylfi Sigurdsson to Everton this week, has beaten United twice in August in the last three years but rarely looked like scoring at Liberty Stadium.
The only time the hosts seriously threatened United was in the third minute when Jordan Ayew broke clear thanks to a fortunate ricochet and curled an attempted cross — with the outside of his right foot — against the crossbar.
United defender Phil Jones also struck the bar in the ninth minute with an effort that came off his shoulder from Juan Mata’s inswinging free kick.
- Four more for Manchester United as Swansea are swept aside at Liberty StadiumEurosport.com
- Paul Pogba survives his biggest Manchester United test vs SwanseaManchester Evening News
- Man Utd's Swansea thrashing proves West Ham performance wasn't just a one-offGoal.com
- Paul Pogba, Romelu Lukaku lead Manchester United to 4-0 win over SwanseaZee News
- Romelu Lukaku joins elite Manchester United group with Swansea goalMetro
- Swansea 0-4 Manchester United: Romelu Lukaku, Paul Pogba and Anthony Martial ...Mirror.co.uk
- Swansea City 0-4 Manchester UnitedBBC Sport
- Lukaku, Pogba and Martial on target again as Manchester United hammer SwanseaYahoo News UK
- F365's early loser: Ander Herrera (but in a very good way)Football365.com