Newcastle twice led through Isaac Hayden and Ayoze Perez, but Gabbiadini's two efforts - the second of which came from the spot - earned Southampton a deserved point as they scored in just their second home game in 10 attempts.
Rafael Benitez will be disappointed with his side having looked on course for all three points, but the North-East outfit have at least stopped a run of four consecutive defeats at the home of the South coast club.
A minute later, Tadic should have headed Southampton in front with a free effort at the back post, and the playmaker was made to pay shortly afterwards when Newcastle went in front.
The ball fell invitingly for Hayden on the edge of the area, and the former Arsenal man took full advantage with a well-struck effort which found the bottom corner from 20 yards out.
The home side went straight up the other end and threatened an immediate equaliser through Virgil van Dijk - making his first start at St Mary's since handing in a transfer request - but the Dutchman's header went just wide of the far post.
During the closing stages of the first half, Southampton threw men forward in search of an equaliser, but a succession of blocks from Jamaal Lascelles and Florian Lejeune preserved Newcastle's clean sheet.
Less than two minutes after the restart, Newcastle struck the bar through a deflected effort from Joselu, and it allowed Southampton to quickly find an equaliser as Gabbiadini held off the attentions of Javier Manquillo before drilling a shot into the bottom corner from the edge of the box.
However, Newcastle quickly regained their led through Perez, who fired the ball inside Forster's near post after the England stopper had failed to hold his initial low strike.
The game was being played at a ferocious pace and just before the hour mark, Newcastle should have been reduced to 10 men when DeAndre Yedlin fouled Nathan Redmond on the touchline, but the referee opted against giving the right-back a deserved second yellow card.
The North-East outfit were less fortunate later in the game when the Saints equalised for a second time, this time from the penalty spot.
Lejeune was correctly adjudged to have fouled Shane Long inside the penalty area, and Gabbiadini made no mistake from 12 yards with his effort being directed into the top corner for just his third goal of the campaign.
Both teams pushed for a winner during the closing stages and it almost came via the head of Lejeune, but the summer signing's effort was brilliantly cleared off the line by Steven Davis.