The Scot was appointed as Uwe Rosler's replacement in midweek despite a Football Association investigation into the alleged sending of derogatory text messages while at Cardiff City.
Wigan chairman Dave Whelan also courted controversy with perceived anti-Semitic remarks made in a newspaper interview but, with attentions returning to on-field matters, Mackay's side made an excellent start.
Shaun Maloney's free-kick 24 minutes in gave Wigan the lead, which they held on to until just before the hour mark, when Chelsea loanee Bamford equalised shortly after coming off the bench.
Second-placed Bournemouth also dropped points as they twice threw away the lead to draw 2-2 against Ipswich Town on the south coast.
Teddy Bishop and Daryl Murphy twice hauled Ipswich level, with the draw allowing Derby County to extend their lead at the top of the Championship to three points.
Goals from Jordan Ibe and Craig Bryson at Vicarage Road helped Derby to a 2-1 win, after Gianni Munari's goal had given Watford hope.
The defeat saw Watford slip out of the play-off spots, with Blackburn Rovers taking their place after a late Jordan Rhodes double condemned Leeds United to a 2-1 loss at Ewood Park.
Souleymane Doukara put the visitors ahead in the first half, but two goals in the final 20 minutes from Rhodes turned the tables and moved Blackburn into sixth, despite Tom Cairney being shown a red card late on.
Birmingham City continued their unbeaten start to the Gary Rowett era, leaving it late to see off struggling Rotherham United 1-0 and move out of the bottom three.
Clayton Donaldson's winner also meant Steve Evans' men slipped into the relegation zone as a result, with fellow strugglers Blackpool and Bolton Wanderers drawing 1-1 in their Lancashire derby at Bloomfield Road.
A flurry of second-half goals helped Nottingham Forest to a 3-0 win over Wolves, as efforts from Britt Assombalonga, Matty Fryatt and Henri Lansbury kept Stuart Pearce's side hot on the heels of those in the play-off spots.
Charlton Athletic shared a goalless draw against Millwall in a disappointing London derby, while Sheffield Wednesday and Huddersfield Town also took a point each from their 0-0 draw in the day's early game.
There was no shortage of goals at Carrow Road, however, as Norwich City shared the spoils with Brighton and Hove Albion in a six-goal thriller that also saw Bradley Johnson dismissed in the latter stages.
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