The Edinburgh outfit arrived in the east end of Glasgow keen to delay the coronation and keep Rangers at arm's length as the two sides battle it out for a Champions League spot.
But Hartson rewarded the faith of his manager in recalling him with a third-minute decider to give Strachan his second trophy in his first season in charge.
Strachan brought back Hartson for Dion Dublin in the only change from the team who won at Livingston.
In contrast, Hearts interim manager Valdas Ivanauskas made five changes from the side who thrashed Edinburgh rivals Hibernian at Hampden Park on Sunday to book their place in the Tennent's Scottish Cup final.
The champions-elect had seven matches in which to get the five points required to lift the coveted trophy but the Celtic supporters arrived at Parkhead expecting their heroes to finish it in style.
And Hartson did not disappoint by giving the home side a dream start.
Maciej Zurawski nodded on a long punt down field from Artur Boruc to the Welshman.
He struck a sweet right-foot shot, which seemed to bounce over the despairing dive of Craig Gordon for his 18th goal of the campaign.
Zurawski picked out his strike partner again in the 12th minute but Robbie Neilson did enough to put him off and this time the Scotland goalkeeper comfortably saved his header from seven yards out.
But Hartson was booked moments later for a foul on the Hearts full-back which almost brought an equaliser against the run of play.
Bednar spun just inside the box and sent a low right-foot effort toward the bottom corner. But Boruc threw himself to clip the ball behind.
Zurawski looked to play Stilian Petrov in the 32nd minute but the ball would not sit for him and Andy Webster made the clearance.
The defender then gave Boruc a scare with a long-range lob onto the top of the net after Stephen McManus had failed to clear the danger.
At the other end Gordon saved Shunsuke Nakamura's 30-yard free-kick after Mikoliunus had handled Hartson's loose pass.
Hearts thought they had an equaliser in the 49th minute when Webster bundled the ball over the line, but the linesman flagged for offside.
Neilson gifted Bobo Balde an unexpected chance to test Gordon in the 53rd minute when he cut out Nakamura's wasted cross but he then gave the ball straight to the defender on the edge of the area.
But it caught Balde by surprise and he rushed his shot and the goalkeeper made an easy save.
Ivanauskas made the first change of the game moments later with Edgaras Jankauskas dazed from a clash of heads with Petrov and on in his place came Michal Pospisil.
Bednar almost shocked Boruc in the 56th minute when he hit a first-time shot towards the far corner of the net, but the flicked the ball wide.
Strachan swapped Nakamura with Stephen Pearson a minute later before Fyssas was booked for a bad challenge on Petrov.
The Hearts bench sensed an equaliser was on the way and they threw on Skacel for Mikoliunas to unsettle the nervy defence further.
The home fans were also getting anxious as Boruc stretched to turn away Skacel's long-range strike and Mark Wilson blocked Deividas Cesnauskis' follow-up shot.
Hartson received a standing ovation when he left the field to be replaced by Dublin in the 70th minute.
But Boruc did nothing for Celtic nerves when he unconvincingly punched a cross away instead of catching it.
The Celtic supporters started to sing about their title success after referee Dougie McDonald rejected Hearts' claims of a penalty when Bednar went down under the challenge of Balde.
The Tynecastle frontman and his team-mates never appealed but Ivanauskas was sent to the stand for his protests.
: Boruc, Telfer, Balde, McManus, Wilson, Nakamura (Pearson 58), Petrov, Lennon, Maloney (McGeady 82), Zurawski, Hartson (Dublin 69).
: Gordon, Neilson, Webster, Berra, Fyssas, Cesnauskis, Hartley, Brellier (Elliot 85), Mikoliunas (Skacel 62), Bednar, Jankauskas (Pospisil 54).
: D McDonald (Scotland).
A dramatic last-gasp win for Hibernian allowed them to race past Kilmarnock into fourth place in the Bank of Scotland Premier League.
Killie had looked set to extend their lead over their hosts to five points when Gary Wales gave them an early advantage. But goals from Derek Riordan and Paul Dalglish in the last 10 minutes handed Hibs a shock win.