Palu's 58th-minute try was the only score in the second half and allowed the Waratahs to recover from a 12-10 halftime deficit to record their second win in three matches in the 2008 season.
But Palu went from hero to villain in a second when, immediately after scoring his try, he punched Highlanders scrumhalf Jimmy Cowan and was shown a yellow card which forced him to spend the next 10 minutes in the sin bin.
Palu's unconverted try was enough to give the Waratahs a win over the Highlanders who endured their third straight loss by six points or less and slumped toward the bottom of the table.
The Highlanders lost 22-16 to the Queensland Reds, 22-20 to the ACT Brumbies and returned to their home ground, Carisbrook, Saturday to suffer their third straight narrow loss to an Australian team, while claiming their third bonus point.
The match was played in sheeting rain which affected handling. The Waratahs eked out narrow advantages of territory and possession but didn't play well.
"The funny thing about this competition is you've got to be able to win when you play badly and we could hardly have played worse so it was good to walk away with the four points," Waratahs captain Phil Waugh said.
The Highlanders capitalized in the first 30 minutes of the match, though they trailed in possession and territory, to lead 12-3 with two first-half tries.
Winger Fetu'u Vainikolo scored in the 15th minute when the Highlanders worked a clever movement from an attacking scrum, screwing the scrum to create a blindside overlap for the powerful winger.
Replacement Adam Thomson then scored a superb try from a controlled kick and chase to score in the 29th minute and to give the Highlanders a 12-3 lead.
Ben Jacobs scored a vital try for the Waratahs three minutes before halftime, pulling them back within two points at the interval, and Palu's late try clinched the Waratahs win.
"We didn't make the most of the ball we had. In these conditions the ball has got to be like gold and we didn't treat it that way," Otago captain Jason McDonald said.
Cards - Tom Donnelly (yellow)
Pen - Kurtley Beale
Cards - Wycliff Palu (yellow)
Venue: Carisbrook, Dunedin
Referee: JC Fortuin (RSA)
15. James Wilson, 14. Paul Williams , 13. Niva Ta’auso, 12. Johnny Leota, 11. Fetu’u Vainikolo, 10. Michael Delany, 9. Jimmy Cowan (VC ), 8. Steven Setephano , 7. Alando Soakai, 6. Hayden Triggs , 5. Tom Donnelly, 4. Isaac Ross, 3. Clint Newland, 2. Jason Macdonald ( C ), 1. Jamie Mackintosh
Reserves: 16. David Hall, 17. Chris King, 18. Adam Thomson, 19. Tim Boys, 20. Toby Morland, 21. Ben W Smith, 22. Brett Mather
Reserves:16. Tatafu Polota-Nau,17. Dan Palmer,18. Dean Mumm,19. Beau Robinson,20. Luke Burgess,21. Sam Harris,22. Alfi Mafi,23rd Man – Pat McCutcheon.