Grimsby, second from bottom of League Two, showed no sign of an inferiority complex against the League One leaders despite having the worst defensive record in their division.
However, Leeds eventually opened the scoring in the 40th minute but had fortune on their side. Max Gradel cleverly beat his man on the left before seeing Grimsby defender Olly Lancashire turn the on-loan winger's cross into his own net.
In first-half injury time, Neil Kilkenny completed a neat passing move by shooting past Nick Colgan from just outside the penalty box to double Leeds' advantage.
Jermaine Beckford then finished a fine run by Bradley Johnson by tucking away the third after 57 minutes as Leeds threatened to run riot.
But a minute later Casper Ankergren punched a clearance straight to Grimsby midfielder and former Whites star Peter Sweeney, who expertly volleyed home to give his side a well-earned consolation.