In-form Blues showed no signs of fatigue in their 44th game of the season as they followed up their impressive FA Cup draw at Chelsea with a deserved victory against Keith Hill's side.
Chris Burke set the ball rolling with an early opener which was deflected in off Tykes skipper Rob Edwards and the impressive Fahey was also on target in the first half after Barnsley's leading scorer Craig Davies' 10th goal of the season had brought the home side level.
Substitute Nathan Redmond sealed the points for Chris Hughton's side with a third goal after great work from Fahey and Burke to leave Blues five points behind second-placed Southampton with a game in hand.
It took Blues just six minutes to take the lead, with Marlon King capitalising on a mistake from Jim McNulty on the touchline and cutting the ball back for Burke, whose goal-bound left-foot shot was deflected in off the head of centre-half Edwards.
But the Tykes were level 18 minutes in, when debutant David Cotterill looked to be upended in the penalty area but after referee Carl Boyeson waved play on the winger picked himself up to cut the ball back for Davies, who drilled home with a clinical right-foot finish.
Burke was giving Tykes left-back Jay McEveley a torrid time and the winger fired over the bar before the impressive Fahey swivelled and fired the visitors back in front with a venomous left-foot drive from 20 yards which in off the far post.
Barnsley's leading scorer Davies was proving to be a handful for the Blues defence and the summer signing from Chesterfield had his head in hands 10 minutes before half-time when his measured right-foot strike rattled the crossbar.
Barnsley were struggling to contain Burke and the former Cardiff man foxed McEveley with an exquisite piece of skill but his cross was deflected away from King as the striker prepared to pull the trigger.
Blues midfielder Jordon Mutch had a lucky escape when he sliced a tame corner from the right just wide of his own goal.
But Hughton's side gave themselves some breathing space with a third goal 13 minutes from time after a brisk break which involved Fahey and Burke, the two best players on the park.
Irish midfielder Fahey was the architect, with a raking long-range pass into the path of Burke and he crossed to the back post where the onrushing Redmond finished emphatically with his left foot just four minutes after coming on as Blues sauntered to a fifth consecutive away win.
Source: DSG