Just when it looked like it would end advantage to Shakhtar, Donati fired into the far corner from a McGeady cross to set Celtic Park alight.
So it was no surprise when the home side made the breakthrough on 54 minutes when Beattie ran on to a McGeady cross and crashed a header beyond McNeil.
BBC: SPORT | Football | Scottish Premier | Celtic 1-0 Hibernian
Vladimir Smicer missed a great chance to score a third after Baros played him through, while at the other end John Hartson headed a McGeady corner wide of Kirkland's goal.
Anthony Stokes had perhaps been harshly penalised for a challenge on Aiden McGeady and a spot-kick was the result.
The hosts pressed for a quick second goal and Aiden McGeady worked himself into a dangerous position, only to loft his cross high and wide.
The Czech midfielder ought to have grabbed himself a second goal in the closing seconds of the half but sent his diving header wide from five yards following a fine Aiden McGeady cross.
However, the Australian striker did make the breakthrough after 79 minutes, stealing in behind his marker to head home from five yards after a cross from McGeady, who had teased his way past two defenders.
Hearts, who at times looked like a side whose season had finished with the clinching of third place last weekend, were being pushed back now and Kello did well to turn a low drive from Aiden McGeady on to the post and wide for a corner.
Kenny Miller took advantage of calamitous Celtic defending to fire Rangers into a two-goal lead and Aiden McGeady's penalty failed to trigger a comeback.
It happened after Fiona McGeady brought a complaint in August 2010 and while an investigation was being carried out.
McGeady missed a penalty in Sunday's 3-3 draw with Falkirk and Tony Mowbray's side have been criticised for some under-par displays.
However, Celtic were denied a cleansweep when Aiden McGeady was beaten to the Young Player of the Year by Kilmarnock striker Steven Naismith.
BBC: SPORT | Football | Scottish Premier | Nakamura takes top player award
The tribunal found Ms McGeady, a lecturer at the North West Regional College, had been victimised because she had brought complaints in the past.
However, referee Steve Conroy ruled that the striker had led with the arm as he challenged McGregor to a miss-hit McGeady volley that flew high into the air.
With the crowd starting to get edgy, McGeady had a great chance to double the Republic's lead on 75 minutes but his flicked shot was inches over the Cypriot bar.
One minute later, Stokes was punished for a dangerous challenge on McGeady in the Hibs penalty area and Robbie Keane stepped up to convert the resulting penalty kick with confidence.
The Greece international latched on to a long ball from McGeady in the 76th minute and collected himself in front of Langfield before casually flicking the ball into the back of the net.
Hearts were dazed and McGeady left a clutch of players in his slipstream as he powered forward and slid the ball through to Fortune, who slotted home Celtic's second to keep up his red-hot recent form.
Celtic restored parity six minutes after the restart when Samaras sent a square ball to McGeady on the right-hand side of the Motherwell penalty area and the Republic of Ireland international curled in a superb shot past Ruddy.
Shortly after the restart, Gary Caldwell powered in a short-range header that worked its way back out of the Dons defence, but Aiden McGeady flighted flighted in a searching cross for Samaras to double Celtic's tally with a cute header from six yards out.
McGeady was in a share of 33rd place - a stroke outside the qualifiers.
The final-hole dropped shot saw McGeady signing for a level-par 72 which left him on five under.
The goal gave the home side a boost, with Aiden McGeady and McDonald striking further shots at goal.
However, there was no place in the squad for Aiden McGeady, with a back injury blamed for his absence, while Andreas Hinkel was also omitted.
McGeady blasted in a dangerous left-footed shot from 25 yards out that caught out Balogh and rebounded off the bar then, 10 minutes later, swerved a shot at the Hearts goal that curled wide.
BBC: SPORT | Football | Scottish Premier | Celtic 2-1 Hearts
But home nerves were considerably eased in the 54th minute as Keane dinked delightfully into the net after McGeady had played a wonderful one-two with Paul Green before playing the Spurs striker into space in the box.
"It can be a good little change because we've been taking a bit of stick, " McGeady said in Dublin.
Strachan half-joked that he'd been named PFA Manager of the Year mostly for his man-management in coping with complex characters such as goalkeeper Artur Boruc, as well as dealing with a frosty relationship with winger Aiden McGeady.
Moments later, McGeady forced Ruddy to parry a chipped shot and fired in with another low strike two minutes later.
Now McGeady, who appeared as a late substitute for the Irish against Jamaica, has set his sights on a regular first team berth at Celtic.
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