Goals from Rene Howe and Craig Stanley were enough to ruin Gritton's day and leave manager Lee Richardson facing more calls for his sacking from the home fans.
Certainly Chesterfield were disappointing, especially in a poor first half, but the Shrimps deserve credit for a solid and resilient display that was rewarded with a deserved victory.
It might have been a different story if Gritton, signed as a replacement for top-scorer Jamie Ward who has left to join Sheffield United, had not wasted a wonderful chance at the start of the second half.
The centre-forward was picked out at the back post by a deep cross, but he somehow managed to put his header wide from close range.
It proved an expensive miss as Morecambe went in front six minutes later when Howe made no mistake with his header.
Stanley picked up the ball on the right and delivered a cross which caught out a Chesterfield defence hoping for an offside flag and Howe dived full length to score his tenth of the season.
Chesterfield had struggled to find any rhythm, but they were level three minutes later when Gritton headed the ball on and when Jack Lester played it back, he fired a low shot from the edge of the area past former Spireites keeper Barry Roche.
Roche was jeered by the home fans throughout the game, but he was never put under any sustained pressure and it was the visitors who created the better openings.
Neil Wainwright should have done better in the 59th minute when he got in on the Chesterfield right only to shoot wide, but he made amends by setting up the second.
This time he pulled the ball back from near the touchline and Chesterfield's defence was nowhere to be seen as Stanley was left unmarked to beat Tommy Lee from eight yards.
Richardson made a double change for the last ten minutes and one of those subs Paul Harsley went close with a 20-yard shot in stoppage time, but Morecambe, who were solid and well organised in defence, stood firm to enjoy a rare success on the road.