It brought about their 14th-successive home league win, breaking a record that has stood since 1969, and also marked their eighth victory in a row from the season's start, another record.
Robert Snodgrass had a weak 61st-minute penalty saved by visiting keeper Owain Fon Williams after John Mullins handled, and Stockport manager Gary Ablett was sent to the stand by referee Danny McDermid for angry comments made at half time.
New York-born striker Grella, deputising for the injured Jermaine Beckford, took just nine minutes to net his first League goal in his first full start for Leeds.
Grella, 22, accepted a short return pass from Bradley Johnson inside the Stockport box and curled an effort into the bottom corner.
Leeds grabbed a controversial second goal in the 37th minute when Snodgrass sent a free-kick into the goalmouth where debutant Leigh Bromby appeared to impede Fon Williams into fumbling, before Slovakian international defender Michalik stabbed home from six yards amid strong protests.