After going unbeaten to lead the league at Christmas, Auckland logged just a single win in their next five matches including a 1-0 home loss to strugglers Perth Glory last week.
It meant Steve Corica's side were in fourth entering Saturday's contest at Mount Smart Stadium.
But three first-half goals earned them three points against the side that had usurped them atop the table, City having enjoyed a seven game unbeaten streak despite an injury crisis.
"We started the season so well and then the last five games weren't as good," Smith told Sky Sport NZ.
"We knew that we had to pick it back up again if we wanted to stay at the top of the table.
"That was the mantra all week."
After struggling at times to get a touch early on, the hosts seized the initiative in the 32nd minute when they forced a turnover at halfway before working the ball forward for Guillermo May, who rocketed home from long-range.
"The momentum flipped once that goal was scored," Corica told Sky Sport NZ.
"Goals change matches.
"The boys started to believe again we could win the game and go on."
Guillermo May delights home fans after scoring the opener. (Shane Wenzlick/AAP PHOTOS)
Auckland then secured their winning margin after City couldn't clear two corners, Nando Pijnaker rifling the ball into the roof of the net in the 41st minute and Max Mata tapping in from close range after Patrick Beach was unable to muscle past Logan Rogerson to punch convincingly clear.
City were able to keep the Kiwi side out throughout the second half but they struggled to create good goalscoring opportunities throughout the 90 minutes.
Aurelio Vidmar's side ended the game with 59 per cent of possession but it took until the 92nd minute for them to produce a shot on target, while it was Auckland who would have more touches in their opponent's penalty area.
The visitors slipped to third on the ladder with the defeat.
But there was a silver lining with the return of Mat Leckie, who got his first minutes since November 10 as a late substitute and almost gave his side a late consolation header cleared off the line by Luis Toomey.
