The 19-year-old narrowly beat her fellow American competitor 13.55 to 13.50 in New South Wales to set up a quarter-final match-up against Australia's Sally Fitzgibbons, who received a bye through to the last eight after topping the heat they were both in.
The fourth stop on the seven-date ASP Women's World Championship Tour saw clean two-metre waves after the stormy conditions of the past few days cleared up.
"Carissa (Moore) has been ahead of me on the numbers since we got on tour," Conlogue said. "It's nice to beat her. She's surfing great this year, I always look forward to watching her surf. Every single time I get to the Quarterfinals I either come up against Carissa or Steph (Gilmore). They have a good heat and I have a good heat, but they get the go ahead from the judges. I'm really looking forward to tomorrow. I'm super excited I won that heat."
Australia's Gilmore will face Malia Manuel in the quarters after she beat France's Justine Dupont 12.50 to 7.00.
Heat 1: Laura Enever (AUS) 11.25 def. Sofia Mulanovich (PER) 4.85 Heat 2: Stephanie Gilmore (AUS) 12.50 def. Justine Dupont (FRA) 7.00 Heat 3: Rebecca Woods (AUS) 8.00 def. Lakey Peterson (USA) 6.55 Heat 4: Courtney Conlogue (USA) 13.55 def. Carissa Moore (HAW) 13.50
QF 1: Tyler Wright (AUS) vs. Laura Enever (AUS) QF 2: Malia Manuel (HAW) vs. Stephanie Gilmore (AUS) QF 3: Coco Ho (HAW) vs. Rebecca Woods (AUS) QF 4: Sally Fitzgibbons (AUS) vs. Courtney Conlogue (USA)