Grella sealed the victory in injury time, condemning Oldham to a third straight home defeat.
Leeds could have gone ahead early through Bradley Johnson, who exploited poor defending but was thwarted by Oldham's debutant keeper Darryl Flahavan.
Oldham then had their best chance of the game but winger Joe Colbeck blew it with a woeful touch after he was gifted possession inside the box.
Leeds took control following Howson's second goal of the season and most Oldham efforts were from outside the box, with midfield trio Dean Furman, Chris Taylor and Alex Marrow all unable to test visiting keeper Casper Ankergren.
The Dane's only real save came midway through the second half as he tipped Taylor's drive around the post. Leeds wrapped up the victory on the break when Grella converted Aidan White's cross from close range.