Auckland boss Corica was shown a straight red card by referee Lachlan Keevers after an outburst from his technical area in the 87th minute.
It is unclear what Corica said, but the Auckland manager is now facing suspension after storming down the tunnel at GoMedia Stadium on Saturday following his dismissal.
Auckland sit second but missed a golden chance to cut the gap on league-leaders Newcastle with Saturday's draw against Victory.
Corica's side are three points behind the Jets, who drew 1-1 with Adelaide on Saturday, with two games of the regular season remaining.
An 82nd minute free-kick from Lachlan Brook helped Corica's side avoid defeat against a Victory team missing talisman Juan Mata.
Victory had twice gone ahead through Franco Lino and then again via Nishan Velupillay after Auckland's Sam Cosgrove hit the net late in the first half.
But Brook scored with a free-kick to secure a draw that does little to help second-placed Auckland's premiership bid and also put a dent in Victory's top-two hopes.
Arthur Diles' side showed plenty of resolve without Mata, going ahead after 23 minutes when Velpuillay and Denis Genreau combined to set up Lino.
Auckland seemed to lose their way after Lino's opener, with Brook booked for dissent and All Whites defender Nadon Pijnaker going off with a shoulder injury.
After Roderick Miranda had cleared a Logan Rogerson effort off the line in the first half, Victory's defence eventually faltered when Cosgrove fired home in the fourth minute of first-half added time.
The Englishman, who moved clear of the golden boot standings with his 12th strike of the season, poked in after Victory failed to deal with a Hiroki Sakai throw-in.
Cosgrove's strike made the halftime score 1-1, but Velupillay was quick to push Victory back into the lead when he seized on some clumsy control from Luka Vicelich and fired beyond the reach of James Hilton.
Brook's set-piece finish drew Auckland level, but Corica's frustrations came to the fore as the Kiwi outfit were unable to fashion a winner.
11°C