The summer signing from FC Twente scored in the win over the Championship side, while Steven Davis and James Ward-Prowse also found the net on Thursday evening
Ronald Koeman's tenure as manager has started promisingly on the pitch, but the exodus of talent from the playing staff has been a significant cause for concern among the St Mary's Stadium faithful.
With Rickie Lambert, Luke Shaw, Adam Lallana Dejan Lovren and Calum Chambers all having left the club, long-serving midfielder Morgan Schneiderlin has been linked with Tottenham, along with Jay Rodriguez.
But Southampton, who handed a debut to Ryan Bertrand, put all that to one side on Thursday as they swept aside their Championship rivals at the AMEX Stadium.
Tadic is proof that the transfer activity has not all been in one direction, the Serbia international having arrived from Twente, and he opened the scoring after 19 minutes with a fine shot on the turn to net his first goal for the club.
The visitors' advantage was doubled on the stroke of half-time as another new arrival, Graziano Pelle, saw his shot fall kindly to Davis to slot home after an initial block.
Bertrand, on loan from Chelsea for the season, was withdrawn at the break after a quiet 45 minutes with his new side, and Ward-Prowse added the third in his absence.
The 19-year-old's strike was the pick of the bunch as he smashed home from 25 yards in the 66th minute, while Kazenga LuaLua became the first player to breach Southampton's defence in pre-season as he grabbed Brighton's consolation late on.