The Serb converted from the spot with 69 minutes gone after Yann M'Vila had tripped Ryan Bertrand to secure a 1-0 victory at the Stadium of Light as the Saints edged a dour contest in which Black Cats keeper Costel Pantilimon had earlier kept them at bay with a string of important saves.
Southampton have collected 14 of the last 18 Barclays Premier league points they have contested, while Sunderland have lost three of the four games they have played under new manager Sam Allardyce.
Having seen his side concede six in kamikaze fashion at Everton last weekend, Allardyce was looking to find a balance between defence and attack, and his hopes of doing so were boosted by the return to fitness of central defender Younes Kaboul and midfielder Ola Toivonen.
He also handed 21-year-old striker Duncan Watmore a first start for the club with Jermain Defoe sitting on the bench despite his goal at Goodison Park.
Watmore in particular started in lively fashion, but it was the Saints who dominated possession with James Ward-Prowse and Tadic linking well with frontman Graziano Pelle.
However, despite enjoying the lion's share of the ball, the visitors were only able to test Pantilimon twice during a drab first half.
The Romanian did well to smother Tadic's 16th-minute shot after he had run on to Pelle's back-heeled pass, and reacted smartly to beat away Sadio Mane's volley six minutes later.
But although Sunderland's rearguard was under pressure for long periods, they managed largely to keep Southampton at bay with Mane particularly wasteful in possession.
For their part, the Black Cats created little of note with keeper Maarten Stekelenburg collecting Kaboul's weak first-minute header with little difficult and seeing Toivonen screw a long-range effort fully 30 yards wide.
Allardyce replaced Toivonen with Fabio Borini at the break and the Italian might have made an early impact, but snatched at a 48th-minute effort and scuffed it straight to the waiting Stekelenburg.
Sunderland were far more positive in the opening stages of the second half, but Pantilimon had to repel another well-struck effort from Mane with 52 minutes gone, and the striker fell over as he attempted to turn in front of goal seconds later.
Kaboul and Billy Jones blocked shots from Mane and Pelle in quick succession, and DeAndre Yedlin needed prolonged treatment after colliding with Mane as he headed off his own line after Jose Fonte had flicked on Ward-Prowse's 56th-minute corner.
Coates came to the rescue five minutes later to block Steven Davis' goal-bound shot with Pantilimon beaten, but Sunderland fell behind with 21 minutes remaining after M'Vila's needless challenge on Bertrand prompted referee Mike Jones to point to the spot.
The keeper guessed correctly as he dived to his left, but Tadic's spot-kick was too firm for him to do anything about it.
The Black Cats' response was immediate with Borini testing Stekelenburg at his near post and Adam Johnson curling a free-kick inches wide, but it proved to be in vain.
TWEET OF THE MATCH
Big Sam had his head in his hands
What a rash sliding tackle
#SAFC - James Hunter (@JhunterChron) Sunderland AFC's football writer for the Chronicle sums up Yann M'Vila mistake after he brought down Ryan Bertrand for the penalty.
Costel Pantilimon: 8
DeAndre Yedlin: 6
Sebastian Coates: 7
Younes Kaboul: 6
Billy Jones: 6
Yann M'Vila: 6
Jordi Gomez (Defoe, 74 mins): 6
Adam Johnson: 6
Ola Toivonen (Borini, 46 mins): 5
Duncan Watmore: 6
Steven Fletcher (Rodwell, 70 mins): 6
Fabio Borini: 7
Jack Rodwell: 6
Jermain Defoe: 6
Maarten Stekelenburg: 6
Maya Yoshida: 6
Jose Fonte: 7
Virgil van Dijk: 7
Ryan Bertrand: 7
Jordy Clasie (Romeu, 78 mins): 6
James Ward-Prowse: 7
Sadio Mane (Jimenez, 83 mins): 6
Steven Davis: 7
Dusan Tadic (Caulker, 90 mins): 8
Graziano Pelle: 7
Oriol Romeu: 6
Juanmi Jimenez: 6
Steven Caulker: 6
Dusan Tadic was at the centre of much of Southampton's better work and calmly converted the decisive penalty.
MOMENT OF THE MATCH
Sebastian Coates' goal-line clearance to keep out Steven Davis' shot with Costel Pantilimon beaten for once.
VIEW FROM THE BENCH
Sam Allardyce will have been pleased with his side's dogged defending six days after they conceded a hatful at Everton, but there remains significant room for improvement
Ronald Koeman will have been disappointed with the finishing which might have cost the visitors victory
MOAN OF THE MATCH
Yann M'Vila's challenge on Ryan Bertrand which led to the penalty was needless and allowed a precious point to slip from the Black Cats' grasp.
WHO'S UP NEXT
Crystal Palace v Sunderland, November 23 (Premier League)
Southampton v Stoke City, November 21 (Premier League)
Source : PA