Turner broke the deadlock 10 minutes into the second half following an error from Clarets’ keeper Paul Robinson.
However, the Shrimps conceded their first pre-season goal midway through the period as Gray fired home from 20 yards.
Having named eight trialists in his squads for the opening pre-season matches, Morecambe boss Jim Bentley went one better last night with nine among his 23-man line-up.
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It was a game with precious little ebb and flow in the first half, understandably so given the stifling heat.
An opening period of few opportunities saw the Shrimps limited to attempts from set pieces and long distance.
Ryan Edwards was off target after Robinson flapped at a fifth minute corner and punched the ball onto the defender’s head.
Seconds later and it was Morecambe keeper Barry Roche who was called into action, keeping out Ashley Barnes’ header.
Roche also did well to thwart Rouwen Hemmings after he had been played in behind the Shrimps’ backline.
At the other end, Robinson pushed Lee Molyneux’s deflected free-kick behind for a corner which Dean Winnard headed over.
Michael Keane did likewise at the other end as the first half drew to a close, after which there were the expected changes from the visitors.
Clarets’ half-time substitute Lukas Jutkiewicz had a couple of early sighters which failed to seriously test Roche.
The deadlock was broken soon afterwards, however, when Robinson spilled Molyneux’s cross and Turner headed home from close range.
Burnley’s increased tempo after the break was rewarded though when Aaron McGowan’s error allowed Gray a sight of goal and he finished clinically.
Bentley took the chance to rotate his line-up as the second half progressed with one replacement, Kevin Ellison, denied a goal for a foul on Tendayi Darikwa.
Both sides continued to hustle and bustle but, ultimately, had to settle for a draw.