The pair were level at two sets each with Wawrinka leading 5-3 in the decider when the match referee decided it was too dark to continue late Sunday on the grass courts of the Royal Sydney Golf Club.
The pair resumed on Monday with the Swiss breaking Hewitt in the first game back to close out the match 4-6, 6-4, 6-7 (9-7), 6-4, 6-3, putting the visitors in the 16-team World Group in 2012.
Wawrinka said he was delighted to be the one to hand his country victory, as opposed to good friend -- and the more celebrated -- Roger Federer.
"It's amazing to be in the same team (as Federer)," he said.
"But in Switzerland it is never easy because it doesn't matter what I am going to do or which ranking I am going to have because it's never going to be enough for Swiss people because they always look to Roger -- but that's okay."
For Australia, it means another year in the Davis Cup doldrums, forced to battle it out in zonal qualifiers for a chance to enter the elite competition again in 2013.
Hewitt came to the court on Monday with a heavily strapped right knee and was cheered by a small group of spectators who turned up for the unexpected extra day.
He raced to a 30-0 lead but appeared to be struggling, with two double faults and two unforced errors ultimately costing him the game.
"I went out there and gave it what I could, but it wasn't to be," said the former world number one.
Wawrinka also played through the pain barrier.
He has been battling a leg injury, but Swiss captain Severin Luthi decided against throwing Marco Chiudinelli or Stephane Bohli into the fire of a fifth rubber and the world number 19 repaid his faith.
World number three Federer had levelled the best-of-five tie at 2-2 when he beat Bernard Tomic in four sets 6-2, 7-5, 3-6, 6-3 on Sunday.
It followed Federer and Wawrinka losing their doubles rubber to Hewitt and Chris Guccione. In the opening matches, Tomic beat Wawrinka while Federer won his clash with Hewitt.
Australia will find out who they play in regional qualifying for 2012 at the draw in Bangkok on Wednesday.