Long, starting up front ahead of Graziano Pelle, put Southampton in front with a header from Matt Targett's cross in the 17th minute.
Tadic came on as a substitute in the 71st and doubled Southampton's lead two minutes later, running into Watford's penalty area, creating some space for himself and finishing low beyond goalkeeper Heurelho Gomes.
Watford was outplayed at St. Mary's Stadium, with its in-form strike pairing of Odion Ighalo and Troy Deeney kept in check.
Related story
Sanchez inspires Arsenal to 3-1 win at Watford
