Scott McDonald netted his 20th SPL goal of the season as Celtic ended a run of four games without a victory.
With half-time approaching, Jan Vennegoor of Hesselink's flick was converted from close range by McDonald.
Soon after, Vennegoor of Hesselink missed with a close range header but made amends when he nodded home Aiden McGeady's 69th-minute delivery.
Georgios Samaras completed the scoring late in the game, steering home another excellent cross from McGeady.
Celtic trail table-toppers Rangers by three points and have played a game more than their Glasgow rivals, who they meet next Saturday lunchtime.
The match was switched to Livingston's Almondvale due to the poor playing surface at Fir Park, where Gretna have been tenants this season.
However, a poor crowd of 3,561 will not have done much to alleviate the ailing club's financial problems.
With Gretna scrapping for every ball, Celtic found it difficult to establish any rhythm in the early stages.
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