Only a last-gasp Mike Harries penalty denied Wales a first international win on Australian soil since 1969 and Howley believes the team that took them so close to success last time out can finish the job in Sydney.
"This Wales team was within around 30 seconds of beating the Wallabies on their home patch for the first time in 43 years," said Howley.
"The challenge now is to go one better than that and make sure we are ahead on the scoreboard, not just when the hooter goes, but when the game finishes this weekend.
"We know what we have to do to beat Australia, but there is a difference between knowing how to win and achieving that aim.
"The players can take some credit for the way they played for the large part of the match on Saturday, but that will be scant consolation if we don't come home with a win in this series.
"We have risen to our highest position (fourth) in the IRB World rankings because of our performances so far this season, which can have positive repercussions for the 2015 Rugby World Cup, but now we want to stay there and that means coming away with the spoils on Saturday afternoon."
Howley makes one alteration to his bench for the last game of a four-match tour that has seen Test defeats in Brisbane and Melbourne and a midweek win over the Brumbies.
Ospreys hooker Richard Hibbard appears to have paid the price for giving away two crucial penalties in the closing stages of the second rubber, with his place in the matchday squad going to Ken Owens, who started the first Test a fortnight ago.
Wales: Leigh Halfpenny;Alex Cuthbert, Jonathan Davies, Ashley Beck, George North; Rhys Priestland, Mike Phillips; Gethin Jenkins, Matthew Rees, Adam Jones, Bradley Davies, Alun Wyn Jones, Dan Lydiate, Sam Warburton (captain), Ryan Jones
Replacements:Ken Owens, Paul James, Luke Charteris, Justin Tipuric, Rhys Webb, James Hook, Scott Williams
NB Bold denotes Lion