They will travel to Christchurch next week to face the Crusaders
The Reds beat the Waratahs 14-12 in a tense Australian derby in Sydney on Saturday to finish the season in fifth place.
This means that they will travel to Christchurch next week to face the Crusaders who finished in fourth after their win against the Hurricanes on Friday.
The Reds needed a determined defensive effort as Wallaby back Berrick Barnes narrowly missed with a penalty attempt and botched a shot at drop-goal after the final siren.
The Reds scrambled home on a try by Ben Lucas and three penalties from Quade Cooper and will have to travel to New Zealand next weekend to stay alive in the title race against the seven-time Super Rugby champion Crusaders.
The Waratahs led 12-8 at half-time, but failed to score a point in the second half as Brendan McKibbin and Barnes missed four shots at goal between them to throw away an Australian derby victory.
Cooper, controversially passed over by former Wallabies coach Robbie Deans in this month's three-Test series against the British and Irish Lions, had a mixed night with a wonderful lofted pass to put Lucas over in the corner in the first half but also made several kicking errors.
Cam Crawford scored his fifth try in five consecutive outings for the Waratahs in the 12th minute before Lucas put the Reds in front 8-7 midway through the opening half.
The Waratahs were reduced to 14 men when hooker John Ulugia was sent to the sin bin after a tackle on winger Rod Davies.
McKibbin latched on to a Cooper pass and broke clear to send Barnes over in the corner to give the Waratahs the halftime lead.
Cooper kicked the Reds into the lead with two penalties early in the second half before a concerted finish by the Waratahs threatened to take the game away from them.
But they defended resolutely with Wallaby flank Michael Hooper prevented from scoring a try in the corner by a combined Cooper-Nick Frisby tackle.
Barnes missed with a long range penalty attempt before narrowly missing another one in the final minute. He then scuffed his drop goal attempt well wide, much to his anguish.
The Waratahs didn't help their winning chances with 15 handling errors and five turnovers.
The Reds are likely to be without flying wing Rod Davies for the rest of the competition after he over-stretched his left knee in a tackle and was helped from the field by trainers in the second half.
It was the Reds' 10th win of the season while the Waratahs bowed out with an 8-8 split in Michael Cheika's first season as coach.
For the Waratahs:
Tries: Crawford, Barnes
For the Reds:
Pens: Cooper 3
Yellow card: John Ulugia (25 mins, dangerous tackle)
Waratahs: 15 Cam Crawford, 14 Tom Kingston, 13 Rob Horne, 12 Berrick Barnes, 11 Peter Betham, 10 Bernard Foley, 9 Brendan McKibbin, 8 Dave Dennis (captain), 7 Michael Hooper, 6 Jed Holloway, 5 Kane Douglas, 4 Sitaleki Timani, 3 Sekope Kepu, 2 John Ulugia, 1 Benn Robinson.
Replacements: Luke Holmes, Jeremy Tilse, Will Skelton, Pat McCutcheon, Mitchell Chapman, Matt Lucas, Tom Carter, Ben Volavola.
Reds: 15 Ben Lucas, 14 Rod Davies, 13 Ben Tapuai, 12 Mike Harris, 11 Luke Morahan, 10 Quade Cooper, 9 Nick Frisby, 8 Jake Schatz, 7 Liam Gill, 6 Eddie Quirk, 5 Rob Simmons, 4 Ed O'Donoghue, 3 James Slipper (captain), 2 Saia Faingaa, 1 Greg Holmes.
Replacements: 16 Albert Anae, 17 Jono Owen, 18 Radike Samo, 19 Jarrad Butler, 20 Beau Robinson, 21 Jono Lance, 22 Dom Shipperley.
Referee: Steve Walsh (Australia)
Assistant referees: James Leckie (Australia), Ed Martin (Australia)
TMO: George Ayoub (Australia)