First-half goals from Grella and Jonny Webb put the Whites in charge, and they were added to in the second period by Nathan Cartman and a further strike by Grella.
As well as American forward Grella, David Lucas, Lubomir Michalik, Alan Sheehan, Peter Sweeney and former England U-21 star David Prutton featured in the Leeds line-up.
Town included Robbie Stockdale, continuing his rehabilitation from injury, as well as young pro's Peter Bore, Danny North and Grant Normington and Frenchman Mickael Buscher.
Grimsby: Montgomery, Stockdale, Thompson, Normington, Hoyte, Gray, Jardim, Polius (Davis), North (Dixon), Bore, Buscher.
Subs Unused: Taylor, Freeman, Parker.
Leeds United: Lucas, Darville, Webb, Michalik (Whitwell), Sheehan, Hatfield, Prutton, Falkingham, Sweeney (Lees), Grella, Cartman.
Subs Unused: R. Jones, Milne, S. Jones.