The 21-year-old produced a super looping header for the Millers' second after Darren Byfield's opener. But then Moore's men had to scrap to the bitter end to preserve their second precious win in four days.
Rotherham, fresh from their victory over Walsall on Saturday, made the perfect start as their hard work and endeavour paid off and they were two goals clear by half time.
Coventry, unbeaten in the previous eight outings, might have profited early on when Rotherham's recalled keeper Mike Pollitt misjudged Craig Pead's awkward cross, but Chris Swailes tidied it up.
The home side had leading scorer Byfield to thank when they led after 14 minutes.
He collected an angled pass from Carl Robinson, produced a smart turn and sprinted 30 yards past the Coventry defence before slotting a cool shot past Gavin Ward for his seventh of the season.
Seconds later Coventry might have levelled when Steve Staunton slipped a clever free-kick to Johnnie Jackson, but his blistering shot cannoned off Robinson and went for a corner.
John Mullin came close to adding a second for the home side when Martin McIntosh headed down a Robinson corner, but the forward hoisted his shot over.
Calum Davenport headed wide and Youssef Safri was off target with his shot before Chris Sedgwick burst into Coventry's area, only to see his shot blocked.
And on 39 minutes Barker produced a superb looping header from Paul Warne's left-flank cross and put the Millers two in front.
After the break Coventry, who had drawn their previous six matches, stepped up a gear.
Graham Barrett had Pollitt fumbling with a fierce shot and the Rotherham keeper had to race out to clear a sloppy back pass from Robinson.
Pollitt then had to smother a dangerous ball after Stephen Warnock's shot was almost diverted in, but Rotherham hung on to make it four games unbeaten.