Having been knocked out of Europe by Danish champions FC Midtjylland on Thursday night, Ronald Koeman’s side could turn their full attention back to a slow start to their domestic campaign.
And, after Norwich had Steven Whittaker sent off for two bookings in a little over three minutes, Southampton whirred into life and eventually ran out 3-0 winners at St Mary’s.
Plenty of talk before the game surrounded the continued absence of Victor Wanyama after Koeman said the midfielder was not “mentally and physically good enough to play” amid reported interest from Tottenham – but it was fit-again Sadio Mane, himself a player in demand, who shone alongside Tadic.
Graziano Pelle opened the scoring in first-half injury time as Mane fed the ball into his path and he also provided the assist for Tadic to double their lead; the game was well and truly over when Tadic turned home from close range moments later.
Norwich goalkeeper John Ruddy was tested in just the second minute with a curling James Ward-Prowse free-kick.
But it was Norwich who passed up the best chance of the opening 20 minutes as Cameron Jerome could not make good enough contact with the ball and headed tamely wide.
Whittaker picked up his first booking for needlessly grabbing Matt Targett and not allowing him to take a quick thrown-in before the hosts came close again as Pelle knocked down a cross into the path of Tadic but the Serbia international dragged his shot just wide.
And Whittaker’s afternoon was over shortly afterwards as he picked up a second booking for holding Tadic and preventing him latching onto a long ball, with Neil reacting by bringing on Andre Wisdom in place of Wes Hoolahan.
Despite introducing another defender from the bench, Neil still saw his side lose the lead in first-half stoppage time as Jonny Howson was caught napping by Ward-Prowse.
He fed Mane, who rolled the ball into Pelle’s path with the Italy international snaffling the chance from close range for his second league goal of the season.
And the same pair nearly linked up for a second on the stroke of half-time but this time Mane’s cross was just out of reach for Pelle.
It was Mane again causing the problems as a Ruddy miscue saw the ball end up at the Senegal international’s feet before he drew another smart save from the Canaries’ stopper.
Half-time substitute Jay Rodriguez was the next man to test Ruddy, who was also equal to his shot as the striker went in search of his first Premier League goal in 17 months.
Ruddy would have been powerless to prevent Pelle adding his second after Mane teed up the busy striker, whose resulting strike from the edge of the box flashed narrowly wide.
The hosts had been threatening a second and it duly arrived with 25 minutes remaining as Tadic, another player showing the form of last season, steered home Mane’s cross from 12 yards.
Tadic needed just three minutes to further extend Southampton’s lead as Pelle’s strong header from Cedric Soares’ cross was kept out by Ruddy, only for the winger to turn home the rebound.