The Bluebirds controlled the majority of play at Oakwell and took the lead when Ben Nugent headed home his first career goal in the 22nd minute.
They doubled their advantage six minutes into the second half when Aron Gunnarsson nodded in another Peter Whittingham delivery.
Barnsley did at least make a game of it when Jacob Mellis tucked home from close range 14 minutes from time, but the visitors held on - despite the late dismissal of Simon Lappin.
Palace surrendered top spot after going down at Elland Road, Luciano Becchio and Paul Green the men on target as Neil Warnock's side kicked off their new era in style after having been bought by GFH Capital this week.
Peter Ramage got a late consolation for the Eagles but they could not find an equaliser.
Leicester climbed to third thanks to their 2-0 triumph at Sheffield Wednesday - while Middlesbrough and Hull were both losing.
Ben Marshall scored one goal and set up another on his return to Hillsborough as the Foxes consigned the Owls to a fourth straight league defeat.
Middlesbrough suffered a surprise 3-1 loss against Bristol City at the Riverside, the lowly Robins ending an 11-game winless run to move out of the relegation zone.
City took a shock lead in foggy conditions through Albert Adomah - a goal Boro goalkeeper Jason Steele will not want to see again - but high-flying Boro drew level before the break when Ishmael Miller netted after a penalty-area scramble.
Shortly after the hour mark Stephen Pearson put the visitors back in front and the victory was sealed with just three minutes to go when substitute Steven Davies netted.
Hull went down 1-0 at home to Burnley, Dean Marney notching the only goal of the game to halt the Clarets' mini slide under new boss Sean Dyche.
In-form Millwall climbed above opponents Blackburn and up to sixth after a 2-0 triumph at Ewood Park.
Chris Wood smashed his seventh goal in seven games 19 minutes from time and James Henry sealed it at the death to extend the Lions' unbeaten league run to 10 games.
Nottingham Forest remained behind the Lions only on goal difference after coming from behind to win 2-1 at Wolves.
Adlene Guedioura marked his return to Molineux with a brilliant long-range winner against his former club, the Algerian settling the game in the 57th minute after Billy Sharp had cancelled out Bjorn Sigurdarson's early opener.
Brighton were made to rue a number of missed opportunities as David Ngog's last-gasp strike earned Bolton an unlikely 1-1 draw at the Amex Stadium.
The former Liverpool striker netted with the last kick of the game to cancel out Bruno Saltor's opener and preserve Dougie Freedman's unbeaten record as Bolton boss following his move from Crystal Palace.
Adam Clayton converted a late penalty to salvage a 1-1 draw for 10-man Huddersfield against Charlton.
The Terriers saw Keith Southern dismissed in the first half and fell behind to Rob Hulse's effort after 60 minutes, but Simon Grayson's men hit back with two minutes to play as Clayton kept his cool to net his first goal in 12 matches.
Blackpool fought back from two goals down to draw 2-2 against Watford.
The Tangerines trailed 2-0 after only 21 minutes through goals from Ikechi Anya and Troy Deeney, but veteran Kevin Phillips threw the hosts a lifeline within seven minutes of the restart and Thomas Ince snatched a point for his team in stoppage time.
The battle between the division's bottom two teams, Ipswich and Peterborough, finished 1-1 at Portman Road.
Lee Tomlin's sixth goal of the season handed the visitors an eighth-minute lead but it was not enough to claim all three points. Tomlin turned villain on the hour as he brought down Lee Martin in the penalty area, leaving on-loan QPR striker DJ Campbell to equalise from the spot.
In the day's late game, substitute Nathan Tyson bagged the winner six minutes from time as Derby bounced back from successive defeats with a 3-2 win over Birmingham.
Tyson put the Rams ahead for a third time after Conor Sammon's two goals were cancelled out by Marlon King's penalty and a Peter Lovenkrands header.