The Hoops will wrap up a hat-trick of Scottish championships with a Glasgow derby win over Partick Thistle at Firhill on Wednesday night, if second-placed Aberdeen drop points at Ross County the previous night.
January signing Johansen headed the first a minute before the break, from a pinpoint Griffiths cross, to open his Celtic account from 10 yards after a cagey opening half.
Griffiths helped himself to the second in the 61st minute after forward partner Stokes had evaded a defender to feed the Scotland international who slid his shot under Marian Kello.
Stokes then struck a third in injury time after being played in by Georgios Samaras to cap Celtic’s 26th Scottish Premiership victory of the season.
Danny Lennon’s St Mirren side remain mired in trouble at the wrong end of the table, in the relegation play-off spot, without a win at Celtic Park since 1990.
However, it was Celtic goalkeeper Fraser Forster who had to make the first real save of the game in the sixth minute when he stopped a low drive by Paul McGowan, after the former Celt had been set up by Conor Newton.
There were few Celtic chances before the first goal arrived though Griffiths, the game’s most influential player, had a drive saved by Buddies goalkeeper Kello and then had the ball in the Paisley side’s net just after the half-hour mark, only to see the flag up for offside.
St Mirren’s valiant first-half effort was undone in the 44th minute when Griffiths went racing down the right before sending in a cross which Johansen only had to guide past Kello for his first goal since signing from Stromsgodset.
Kello then saved from teenage midfielder Liam Henderson seven minutes into the second half, by which time Celtic were turning the screw.
Neil Lennon’s side made sure of the points when Stokes’s pass to Griffiths was confidently slipped past Kello (61) before top-scorer Kris Commons had a shot saved by the Saints keeper ahead of crashing an angled drive back off a post.
In the 71st minute Stokes headed into the net from an Adam Matthews cross but Commons was penalised for his challenge on Kello.
Griffiths then missed a great chance in 10 minutes later when he was set up inside the penalty box by skipper Scott Brown, all too casually chipping the ball over Kello but also wide of the far post.
Returning Celtic defender Virgil van Dijk had the ball in the net from a Stokes cross only to be ruled offside before substitute Teemu Pukki, on for Commons, drove wide of the target.
There was still time for Republic of Ireland striker Stokes to drill the ball low past Kello from the edge of the box for a sweet third (90).