Goals from Leigh Griffiths, his first since arriving from Wolves in January, and Teemo Pukki were enough to see off rock-bottom Hearts and increase Celtic's lead at the summit to 24 points.
Yet goalkeeper Forster commanded much of the attention as he surpassed a record that had belonged to Bobby Clark since the 1970-71 season.
In keeping a 13th successive Scottish Premiership clean sheet, Forster made it 1,215 minutes since he last let in a goal, against Aberdeen back in November.
Celtic have won 15 league matches in a row and saw nearest rivals Aberdeen suffer a surprise 3-1 defeat at 10th-placed Partick Thistle.
Barry Robson missed a first-half penalty for the visitors, who then fell behind when Conrad Balatoni scored just before the hour mark.
Lyle Taylor added further goals either side of Adam Rooney’s reply for Aberdeen, enabling Partick to register a long-awaited first home league win of the season and climb above Saint Mirren into 10th.
Saint Mirren tasted defeat for the fourth successive game as Ross County claimed a 2-1 win in Dingwall.
Yoann Arquin and Melvin de Leeuw grabbed the goals for the victors, the latter scoring with seven minutes remaining after John McGinn had equalised midway through the second half.
Elsewhere, Danny Haynes scored his first goal for Hibernian in a 1-1 draw with Kilmarnock at Rugby Park.
The striker, on loan from Notts County, cancelled out Rory McKenzie's opener to keep Hibernian five points above their opponents.
Hibernian are now level on points with sixth-placed St Johnstone, who lost 1-0 at home to Inverness Caledonian Thistle courtesy of Gary Warren's 42nd-minute header.
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