Watt, 18, produced a brilliant piece of skill, a good turn of pace and a composed finish in the 24th minute to add to Victor Wanyama's early headed opener.
Charlie Mulgrew fired Celtic three ahead just after the break and Watt was on hand to make it 4-0 in the 64th minute.
However, the Hoops switched off the final 10 minutes and Ross Draper scored two consolations.
Dundee United's hopes of maintaining their 100% record and top spot were undone by poor second-half defending as they went down 3-1 at Kilmarnock.
A comedy of errors inside the first five minutes allowed Rory McKenzie and Borja Perez to claim their first goals for Killie before Jude Winchester grabbed the home side's third inside 10 minutes to give Kenny Shiels' side their first win of the season.
Jon Daly pulled one back for the Tannadice side but it was too little, too late.
Hibs made it back-to-back SPL wins with a 2-0 success against St Johnstone at Easter Road.
The home side were second best throughout the first half but took a half-time lead thanks to a 45th-minute goal by Paul Hanlon. Eoin Doyle added the second six minutes after the restart.
Finally, a Richard Brittain penalty was enough to give Ross County their first SPL win of the season - 1-0 at Dundee.