Alty mounted a stern rearguard action to frustrate a Cambridge side who went into the game as Blue Square Premier's top scorers, having hit seven against Forest Green at the weekend.
Said Heathcote: "For us to have kept a clean-sheet against such a prolific side is extremely satisfying.
"The lads can be really proud of their performance."
Meanwhile, Stalybridge did both themselves and neighbours Droylsden a big favour ahead of their derby date at Bower Fold on Saturday.
Bridge won 3-1 at Eastwood to prevent the Nottingham side knocking the Bloods off the top of Blue Square North.
Joe O'Neill, Connor Jennings and Dave Hankin were on target for the slick Celts as they stretched their unbeaten run to five to climb to ninth in the table.
It was a good night, too, for Northwich as they hoisted themselves four points clear of the bottom with an impressive 2-1 victory at AFC Telford.
Jonny Allan netted their 66th minute winner after Vics had earlier let slip a lead given them by Mark Danks on 11 minutes.
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