The Chilean, who led his side to four victories during the period - and within two points of Arsenal at the top of the table - becomes the first manager to win back-to-back awards since Carlo Ancelotti achieved the feat with Chelsea in 2011.
January also saw City advance to the fourth round of the FA Cup while securing their place in the Capital One Cup Final.
Adam Johnson picked up the January award for Barclays Player of the Month following an impressive period with rejuvenated Sunderland.
The winger, who is being widely tipped for a recall to Roy Hodgson's England squad, scored a hat-trick in the 4-1 victory at Fulham before hitting the equaliser in a 2-2 draw with Southampton.
And he completed the month by taking his goal tally to five with the winner against Stoke City, a result which lifted Gus Poyet's side to 14th in the Barclays Premier League table.
"I've been working hard and everything has clicked and fallen back into place again," Johnson told Sky Sports News.
"The highlight of the month was definitely the hat-trick at Fulham which set me off on this good goal-scoring run and the goal against Stoke, which earned us a 1-0 victory, was also huge."
Hear more from the Sunderland winger in Weekend Warm-Up this evening on Sky Sports News from 6.00pm