Chelsea fell to defeat for the seventh time this season in the Premier League as Southampton came to west London and took all three points back down to the south coast.
Both sides came into the game having won their previous game - both being on the road - and it was the Saints who came out on top at Stamford Bridge.
Obafemi and Nathan Redmond either side of the half were the difference for Southampton, as Hasenhüttl's side climb up to 14th in the Premier League.
GOAL! CHELSEA 0-1 SOUTHAMPTON [OBAFEMI 31']
Southampton didn't have much possession, but they punished Chelsea's inability to convert dominance of the ball into a goal, as Obafemi put the visitors ahead just after the half hour mark.
They dispossessed Callum Hudson-Odoi on the touchline, and Højbjerg played in Obafemi. Fikayo Tomori was unable to intercept the pass, and he ran at Kurt Zouma. Cutting inside to the left, the 19-year-old put it past Kepa Arrizabalaga to put the Saints into a shock lead.
GOAL! CHELSEA 0-2 SOUTHAMPTON [REDMOND 73']
Chelsea continued to chase the game as time ticked away in west London, but Nathan Redmond punished the hosts, and all but secured the victory following his finish following a superb Saints move.
A patience Saints knocked the ball around; Armstrong gave a give-and-go with Danny Ings and then the Scot flicked it past Antonio Rudiger to find Nathan Redmond free. The Englishman got to the ball before Kepa Arrizabalaga, and poked it into the empty net.
Southampton's win secures them consecutive away wins in the Premier League, whilst Chelsea lost at home in the league consecutively for the first time since 2011.
An excellent away performance from the Saints, one Chelsea would be proud of on the road, and they got their just reward - three points.
Chelsea found it difficult to break the visitors down - at points look scared to shoot but with no Shane Long, and benching Danny Ings - two of their biggest assets, Ralph Hasenhüttl will be ecstatic.