Celtic remain three points clear at the top of the Scottish Premier League after both they and Rangers won on Wednesday night.
The defending champions eased to a 4-0 victory at home to bottom-club Falkirk while title rivals Rangers secured a 2-1 win at second-bottom St Mirren.
Gary Caldwell converted a 29th-minute opener after a slow start by Celtic and both Jan Vennegoor of Hesselink and Stephen McManus hit the bar just before the break.
Vennegoor of Hesselink then scored his second goal in five days in the 62nd minute to set Celtic on course for their third straight home win.
Aiden McGeady and Darren O'Dea - with his first league goal of the season - then struck in the last 12 minutes to seal a comfortable victory.
However, the three points came at a cost as striker Georgios Samaras limped off and midfielder Scott Brown picked up a yellow card which could rule him out of the last Old Firm derby of the season.
In a dress rehearsal for the Scottish Cup semi-final, Kris Boyd gave Rangers a 12th-minute lead at St Mirren by firing in his 26th goal of the season.
Maurice Edu then put the Gers firmly in control by heading home their second goal just seven minutes later.
The American midfielder has filled the void left by deposed skipper Barry Ferguson and responded with his first goal for the club.
Saints managed to pull a goal back through Andy Dorman in the 56th minute but the visitors held on to keep the pressure on the league leaders.
The Gers also added to a lengthy casualty list, though, with both DaMarcus Beasley and Sasa Papac forced off through injury.