Having started on the bench in the drubbing by West Ham, Moore was back in the Wrexham starting line-up.
And the Wales forward fully demonstrated his importance to Parkinson’s methods.
He held up the ball well, made numerous timely defensive interventions and took his goal in typical fashion.
Moore was at his monstrous best in the memorable wins against Coventry, Sheffield United and Ipswich Town last season.
Now with three goals to his name going into the first international break of the season, the 34-year-old was fully deserving of his ovation when withdrawn in the second-half.
As for the Saints, they will likely feel they did enough to leave north Wales with all three points.
Indeed, the visitors had 67% possession, 19 shots, 11 more than Wrexham, and seven shots on target.
Cyle Larin, Ward-Prowse, Ryan Manning and Azaz all had chances as Wrexham had to dig deep at times.
But Eckert will no doubt be targeting defensive improvements after his side conceded for the eighth Championship match in succession.
If the issues at the back can be resolved, Southampton will undoubtedly be serious automatic promotion contenders. But until then, they will likely continue to come unstuck from time to time.