With Rangers not playing Falkirk until Sunday, the champions knew they could pile the pressure on their rivals and it took just four minutes for Samaras to score his first in three months when he chipped Sean Murdoch before Aiden McGeady doubled Celtic's lead.
A great individual goal from Samaras made it three before Vennegoor of Hesselink tapped in the fourth to get on the score sheet for the first time since September and seal the win for the Hoops. "It's a cliché, but we had to do our stuff today and we did it with real class and professionalism," said Celtic manager Gordon Strachan. "I thought for the players to be dotted all around the world and only have 15 minutes yesterday to try and get a shape on the team, they were terrific."
Hamilton coach Billy Reid said his side could not be judged on games against the Old Firm. "I think today we had nothing to lose and no-one expected us to win," he said. "I was disappointed with the first two goals and the third killed us off."
Celtic looked the hungrier side from the start in their first match at Parkhead since February and Irish international McGeady was soon terrorising the Hamilton defence down the left wing. It took just four minutes for the Hoops to take the lead with striker Samaras scoring his first league goal in three months. Andreas Hinkel played a neat pass to the Greek international who skipped past Martin Canning to chip advancing keeper Sean Murdoch.
Hamilton's Joel Thomas tried his luck when the ball broke to him at the edge of the box in the 12th minute but his effort never troubled Artur Boruc as it trundled past the post. McGeady doubled Celtic's lead in the 22nd minute after great vision from Shunsuke Nakamura.
The Japanese international sent a lofted ball over the top of the Hamilton defence to beat the offside trap and McGeady took a touch before sending an angled shot into the bottom corner of the net. McGeady should have had his second in the 30th minute after great work on the half-way line by Samaras sent him clear but his effort was blocked by Murdoch at the edge of the box after the keeper had rushed out to meet him.
Celtic again piled the pressure on Hamilton at the beginning of the second-half and stretched their lead in the 66th minute when Samaras got his second. He collected a pass on the left and used his pace to beat the Hamilton defence before dragging the ball past Murdoch into the far corner of the net.
Vennegoor of Hesselink had the simplest of tasks to make it 4-0 when Hinkel raced down the right and cut it back for the Dutchman to tap in from a couple of yards out.
At Tannadice, a Colin Nish double wasn't enough for Hibernian as Dundee United recovered from finding themselves 2-0 after ten minutes to secure a 2-2 draw thanks to a late David Goodwillie equaliser.
A Calum Elliot double helped Hearts come from behind to defeat Kilmarnock 3-1. Inverness Caledonian Thistle eased their relegation fears with a 2-1 over fellow strugglers St Mirren. Motherwell and Aberdeen drew 1-1 at Fir Park.