Alty were full value for the point secured by sub Joe O'Neill's 25th minute strike and could even have taken all three had it not been for the brilliance of Burton's veteran keeper Kevin Poole.
Said Heathcote: "For us to have matched the best team in the league on their own ground underlines just how much we've progressed this season and the fact we're disappointed not to have won speaks volumes."
O'Neill, who replaced the injured Colin Little after just eight minutes, gave Alty a deserved lead when his fierce drive from the edge of the box squirmed through Poole's fingers.
But Poole was otherwise Burton's hero, denying Dale Johnson, Shaun Densmore and Greg Young with super saves, enabling the title-chasing hosts to escape with a draw in their first home league game under new manager Roy McFarland.
Meanwhile, bottom-of-the-table Northwich were pitched ever nearer towards relegation as they fell to a sixth consecutive league defeat in tumbling 3-0 at Weymouth.
But there was better news for beleagured Vics off the field with their Manchester-based chairman Jim Rushe announcing he's confident of striking a £1.5m deal to safeguard the the club's long-term future.
The stadium is being sold to pay off creditors of a company owned by former Vics chairman Mike Connett, who last weekend prevented Northwich from playing there by locking himself in, forcing them to switch their home game against Histon to Altrincham.
Elsewhere, Stalybridge's promotion hopes suffered a set-back as they crashed 4-1 to visiting Workington, but Droylsden stepped up their challenge for a place in the play-offs with goals by Tony Gray (2), Jamie McGuire and Kevin Townson giving them an easy 4-0 win at Redditch.
Relegation-haunted Hyde are now next-to-bottom following a 2-1 home defeat by leaders Tamworth.
FC United's run of three straight UniBond premier victories was halted in a 2-1 loss at Witton, who snatched the points with a last-minute Neil Black winner after the rebel Reds' debut-making ex-Leigh striker Tris Whitman had cancelled out Lee Thompson's headed opener.
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