The success has left Brendan Rodgers's side top of the division, six points ahead of second-placed Rangers with just two games left to play, and the Bhoys also have a better goal difference than the Gers.
As a result, Rangers will need to win their last two league games of the season and hope that Celtic lose their last two to have a chance of securing the title, while there will also have to be a fairly significant swing in goal difference, with Celtic's seven better at this stage.
All three goals came in the first period, while Rangers had John Lundstram sent off in the closing stages of the first period at Celtic Park and were ultimately unable to recover.
Celtic closing in on Scottish Premiership title
The warning signs were there for Rangers inside the first minute, with the away side's goalkeeper Jack Butland somehow preventing John Souttar from turning a James Forrest cross into the back of his own net.
Rangers were certainly a threat, though, with Fabio Silva dragging one just wide of the post, before the forward planted a close-range header wide of the post when he really should have scored.
Butland made another excellent save to deny Kyogo Furuhashi just past the 30-minute mark, but there were incredibly three goals and a red card before the end of the first period.
Celtic made the breakthrough in the 35th minute through Matt O'Riley, who drilled a brilliant strike into the bottom corner after controlling a pass from Callum McGregor.
Three minutes later, it was 2-0, with Lundstram turning a cross from Daizen Maeda into the back of his own net, and it was a long way back for Rangers at that stage.
In the 40th minute, it became a 2-1 game, with Cyriel Dessers's close-range header nestling in the back of the net, but the action at the end of the first period had not finished.
Rangers could not respond after Lundstram red card
Indeed, Rangers were reduced to 10 men shortly before the half-time whistle, with Lundstram giving his marching orders for a heavy challenge on Alistair Johnston; the initial decision was a yellow card, but it was upgraded to a red following advice from VAR.
Celtic were awarded a penalty early in the second period when O'Riley was brought to the ground by Mohamed Diomande, but the midfielder saw his effort kept out by Butland.
Maeda then had a goal disallowed for offside just before the hour, but Celtic ultimately did not need another to secure all three points in the Old Firm derby.
There were seven additional minutes at the end of the 90, and Rangers were committing so many players forward, but it was not to be for Philippe Clement's side, who are now all but out of the title race.
Celtic will be confirmed as champions on Tuesday if Rangers fail to beat Dundee, or they can win the title on Wednesday evening with a draw or a win over Kilmarnock.