The league leaders saw off St Johnstone 3-1 courtesy of winger Mackay-Steven's first goals since a 2-1 win over Dundee in April.
Steven MacLean levelled for the visitors after Mackay-Steven had handed Celtic the early lead, but after that the table toppers took control.
Stuart Armstrong's strike sent Celtic into a 2-1 half-time lead, before Mackay-Steven claimed his second to settle the tie.
Basement club Dundee United claimed their first league win since October by thrashing Kilmarnock 5-1.
The resounding victory still leaves Dundee United trailing their closest rivals by nine points in the standings.
Blair Spittal took his tally to four goals in as many games in all competitions with a vital brace, while defender Mark Durnan claimed his first goal since his summer switch from Queen of the South.
Midfielder John Rankin ensured Dundee United took a 4-0 lead into the break, before Sean Dillon completed the rout.
Josh Magennis found the net for Kilmarnock but by that stage the damage had already been inflicted.
Ross County leapfrogged St Johnstone into fourth place thanks to a 2-1 win at Motherwell, as Jackson Irvine and Brian Graham scored the goals.
Craig Curran claimed his eighth goal of the campaign for Motherwell in time added on.
Inverness Caledonian Thistle and Partick Thistle played out a goalless draw, with both sides still fighting for mid-table security.
Source : PA
Source: PA