Tomas Cvancara marked his home debut with the breakthrough goal as Celtic held off a stubborn Falkirk challenge to move second in the Scottish Premiership.

Czech striker Cvancara, signed on loan from Borussia Monchengladbach, glanced in a brilliant header to open his Celtic account before Benjamin Nygren's whipped effort gave the hosts daylight in the second half.

Victory moves Celtic above Rangers on goals scored, and ensures Martin O'Neill remains unbeaten domestically since returning to the dugout, although they are still six points behind leaders Hearts.

When these two sides met in Falkirk a few weeks ago, Celtic were considered a little lucky to come away with a 1-0 win.

This time they were simply more clinical than their visitors, who had more shots and carried a threat throughout in a brave, battling performance.

It took a while for O'Neill's side to click and Falkirk almost took advantage when they had chances though Barney Stewart and Louie Marsh, but both were well saved by Kasper Schmeichel.

Once Celtic got their second, their tails were up and they almost had a third through Nygren, but Scott Bain produced a fine save.

Sebastian Tounekti also had the ball in the net, but Daizen Maeda was offside earlier in the move when he blocked the ball on the goalline.

As has often been the case under O'Neill's interim stewardship, Celtic weren't great but found a way to win.

It was Falkirk who edged the attacking stats - including the xG, 1.07 to Celtic's 0.61 - and they'll feel hard done by to come away with nothing.

But eight league wins from nine for O'Neill is hard to argue against and, while they were a little ropey at the back at times, it was another clean sheet at home. In fact, Celtic are yet to concede at Parkhead with O'Neill at the helm.

That was arguably the most prescient challenge he faced when he came in. Under Wilfried Nancy, Celtic were leaking like a sieve and now they have shut up shop, conceding just three goals across O'Neill's time in charge.

The other big issue was finding a striker. Cvancara was not a name known to many, but a little digging revealed a character not too popular in his last dressing room.

He had two goals from 13 appearances and limited minutes in Germany, yet he has hit the ground running at Celtic and given fans belief he could be the man.

After setting up Yang against Hearts, the 25-year-old led the line again and took his goal superbly, peeling off his marker and glancing a header just out of reach of a despairing Bain.

Falkirk are the feelgood story of the Premiership and they continued to impress, albeit leaving with nothing.

They matched Celtic, whose budget dwarves their own by multitudes, for large spells. Plenty players in this Falkirk squad were playing League One football just two seasons ago, remember.

Calvin Miller was one of those. Previously a highly-rated youngster at Celtic, he played with a point to prove. Barney Stewart, playing university football a little over a year ago, led the line well and on another day could have scored.

While there are a few other candidates for manager of the season at this stage, John McGlynn is one of the favourites. Sitting sixth, Falkirk are not out of place in the top half.

Celtic manager Martin O'Neill: "I thought it was a great win for us, particularly after Thursday night and the effort the players put into that win.

"You could see there were periods in the game where we didn't have the energy, but there's a great camaraderie about the group. They want to go beyond the call of duty and it was a big, big win.

Falkirk manager John McGlynn: "I thought our performance was good. On another day we walk away from here with a point, maybe more if we take the lead.

"We've got a five-point gap [to seventh]. We have to do our best to pick up more points. The squad we've got is a good squad and we're happy to go forward with it."

Celtic visit Aberdeen in the Premiership on Wednesday night, while Falkirk travel to Livingston (both 20:00 GMT).