Chelsea suffered more woe at Stamford Bridge after losing 2-0 to Southampton on Thursday.
Frank Lampard's side have now lost six matches at home in all competitions this season. Chelsea remain in fourth despite the defeat but they are only three points above Tottenham.
Chelsea defender Antonio Rudiger was selected in the starting lineup after he was subjected to racist abuse in Sunday's match against Spurs.
The visitors took the lead from a counter attack after 31 minutes when Obafemi produced a fine strike into the top corner.
Southampton scored a second after 73 minutes after Redmond capped off a fine passing move and chipped the ball over Arrizabalaga.
Chelsea face a London derby away at Arsenal on Sunday, while Southampton welcome Crystal Palace on Saturday.
"It's the same story as a few of the last home games," Lampard said. "We have to work, break defensive lines and do more in an attacking sense.
"If we want to stay [in the top four] we have to win more than we have done recently at home."
Hasenhuttl ran onto the pitch to celebrate at full time and was hailed by Saints supporters long after the final whistle after going over to them.
"You can have a tactical plan but without passion it doesn't work," Hasenhuttl told reporters.
"We stayed brave, tried to keep them far away from our goal and it was by far the best performance this season.
"There's still a long way to go, but in the first two or three months we played like a relegation team, now we're playing like a Premier League team."