Hearts were battered in the first half, Livingston hassling, harrying and dominating. Only an incredible triple save from Gordon kept the scores level.
Neilson hooked Ben Woodburn in the 29th minute, bringing on Peter Haring to stiffen up the midfield and stem the tide on Livingston attacks. It worked.
The visitors were much better in the second half and Liam Boyce latched onto to Barrie McKay’s pass to score the winner. It could have been more. But Livingston could have equalised too.
After going with four at the back against Celtic, Neilson reverted back to his favoured and familiar 3-4-3 formation.
Aaron McEneff kept his place in the centre of midfield with Peter Haring dropping to the bench and Alex Cochrane coming back in at left wing-back.
Boyce was restored to the attack, supported by Woodburn and Barrie McKay.
After scoring, the Irishman was taken off as a precaution after feeling his calf and Michael Smith suffered a back spasm after 15 minutes, forcing his withdrawal. Taylor Moore replaced him at right wing-back.
Player ratings scale - 10: One of best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: Terrible day at office. 2: Abysmal. 1: One of worst performances you've seen.