Match ends, Southampton 0, Stoke City 1.
Stoke continued their impressive run as Bojan's brilliant finish earned a hard-fought win over Southampton.
The Spaniard beat Maarten Stekelenburg with an impudent flick from Erik Pieters' searching left-wing cross.
Dusan Tadic fired narrowly over for Southampton, who created few clear chances, before Stoke saw Ibrahim Afellay's shot cleared off the line.
The Potters climb into the top half after their fifth win in seven league matches.
Southampton, meanwhile, drop to eighth after they saw their own six-match unbeaten run end with a curiously ineffective performance.
Ronald Koeman's side enjoyed long periods of dominance but only tested Jack Butland with one of their 16 efforts.
Stoke trio subdue Saints
The hosts started brightly, with Tadic, arguably their brightest performer, fizzing an angled drive wide after just six minutes.
But they never recovered from conceding their first first-half goal in five matches, as Virgil van Dijk failed to track Bojan's run.
Defensive solidity had been at the heart of Saints' recent good form but they struggled to deal with the threat posed by Stoke's attacking midfield trio of Bojan, Marko Arnautovic and Xherdan Shaqiri, who had nine shots between them.
Shaqiri had an effort well blocked by Maarten Stekelenburg after neat interplay with Bojan, then fired wastefully over after excellent play from Arnautovic.
The Austrian, playing on the left wing, had the better of Southampton right-back Cedric throughout and also set up Afellay's late chance after bulldozing his way into the area.
Potters continue miserly away run
After a poor start to the season, Stoke's gradual climb up the table has been built on defensive solidity and excellent away form.
Once famed for their reliance on results at the Britannia, the Potters have turned themselves into a formidable force on the road under Mark Hughes, with this win taking their tally from their last four home games to 10 points.
They produced a classic away performance in the second half, absorbing wave after wave of Southampton pressure and threatening sporadically on the break.
Stoke had one moment of good fortune, when Philipp Wollscheid felled Graziano Pelle in the area and was lucky to see Lee Mason wave away Southampton's claims for a penalty.
But that aside, they never looked like conceding their first away goal since September 12, and fully deserved to record their first win at Southampton for 35 years.
Man of the match - Marko Arnautovic
What they said
Southampton manager Ronald Koeman: "It was not good enough in the first half. I think it was partly because of the minute's silence for what happened last week. The atmosphere in the stadium was not normal.
"In the second half, we played better, it was a good reaction, but I have to recognise that best chances in the game fell to Stoke."
Stoke manager Mark Hughes: "We're delighted - it's an important win for us. We could have finished off more of our chances but overall it was a good performance from us.
"I think in terms of clear-cut chances we were miles ahead of Southampton. I don't think Jack Butland had a save to make and that's illustrative of how well we played - and we broke with real purpose too."
The stats you need to know
- Stoke have kept five clean sheets in their last six Premier League matches - after conceding in each of their eight league games prior to this run
- Their run of four successive clean sheets away from home is their best in the top flight since February 1970
- There have been just 23 goals scored in Premier League games involving Stoke this season; fewer than any other side
- Southampton's defeat was only their second in their last 11 Premier League games (W5 D4)
Stoke visit Sunderland next Saturday, while Southampton face a trip to Manchester City - without striker Pelle, who picked up his fifth booking of this season in this match and will serve a one-match suspension.
- 2Cédric SoaresSubstituted forJuanmiat 85'minutes
- 6José Fonte
- 17van Dijk
- 4ClasieSubstituted forManéat 64'minutes
- 8DavisSubstituted forWard-Prowseat 72'minutesBooked at 77mins
- 19PellèBooked at 90mins
- 22ShaqiriSubstituted forAfellayat 65'minutes
- 27BojanSubstituted forCameronat 71'minutes
- 19WaltersSubstituted forDioufat 87'minutes
- Lee Mason
- Shots on Target
Second Half ends, Southampton 0, Stoke City 1.
Graziano Pellè (Southampton) is shown the yellow card.
Hand ball by Graziano Pellè (Southampton).
Attempt missed. Ibrahim Afellay (Stoke City) left footed shot from the left side of the box misses to the right. Assisted by Mame Biram Diouf.
Sadio Mané (Southampton) wins a free kick on the right wing.
Foul by Erik Pieters (Stoke City).
Attempt missed. Victor Wanyama (Southampton) left footed shot from outside the box is high and wide to the left. Assisted by Graziano Pellè.
Attempt blocked. Ibrahim Afellay (Stoke City) right footed shot from the centre of the box is blocked. Assisted by Marko Arnautovic.
Attempt missed. Graziano Pellè (Southampton) right footed shot from a difficult angle on the right is close, but misses the top right corner. Assisted by Sadio Mané.
Substitution, Stoke City. Mame Biram Diouf replaces Jonathan Walters.
Attempt missed. Jonathan Walters (Stoke City) header from the centre of the box misses to the right. Assisted by Marko Arnautovic with a cross.
Substitution, Southampton. Juanmi replaces Cédric Soares.
Corner, Southampton. Conceded by Erik Pieters.
Attempt blocked. Shane Long (Southampton) left footed shot from the right side of the box is blocked. Assisted by Graziano Pellè.
Attempt missed. Ibrahim Afellay (Stoke City) right footed shot from the right side of the box is close, but misses to the left. Assisted by Marko Arnautovic.
Attempt missed. Charlie Adam (Stoke City) left footed shot from outside the box is too high. Assisted by Marko Arnautovic.
Attempt missed. Jose Fonte (Southampton) header from the centre of the box is close, but misses to the left. Assisted by James Ward-Prowse with a cross following a set piece situation.
Cédric Soares (Southampton) wins a free kick on the right wing.
Foul by Charlie Adam (Stoke City).