Ramon Tribulietx's men prevailed after regulation and injury time finished scoreless, dumping out Moghreb in Rabat on Wednesday.
Mehdi Khallati missed the decisive spot-kick for Moghreb, after team-mate and goalkeeper Mohamed El Yousfi had brought his side back in it by saving Auckland's fourth penalty kick, taken by Mario Bilen.
El Yousfi's save on Bilen helped square the shoot-out at 3-3 after four kicks each, as Ahmed Jahouh had the first penalty of the shootout saved by Auckland custodian Tamati Williams.
Sanni Issa put Auckland back in front at 4-3, before Khallati's kick came back off an upright to send the New Zealand club through to a last eight clash with ES Setif on Saturday.
Moghreb boss Abdelaziz El Amri introduced Zaid Krouch at the interval in an attempt to increase his team's attacking potency, but it was Auckland who - once again - began the half strongest.
The locals made much of the running in extra time, with Salman Ouald El Haj fouled on the edge of the area by Angel Berlanga - the Spaniard earning the first and only yellow card of the contest.
Moghreb could not create any danger from the free-kick, Ahmed Jahouh's effort blocked by the wall, before Auckland had a fine chance in the second half of the additional 30 minutes to steal victory.
De Vries' cross to the back post found Berlanga, who powered a header wide of the target.
It did not matter, though, as Auckland advanced following a thrilling shootout.
