Eastwood, 24, left Molineux in the summer in a £1.5million move to the Ricoh Arena and it is already looking like money well spent.
Eastwood scored one and made the other as the Sky Blues continued their fine run at Oakwell.
They had walloped Barnsley 4-1 on the opening day of last season - and they again spoiled the party by winning the Tykes' first home game of the new campaign.
Eastwood's performance brought a glowing tribute from his manager Chris Coleman, who said: "Freddie has that little bit extra special something that we haven't got in the rest of the squad.
"He can create something out of nothing and also score a goal out of nothing.''
Eastwood did just that in the 12th minute to put Coventry ahead in their first real attack.
He drilled in a left-foot shot that eluded strike partner Clinton Morrison and went straight in unaided.
Barnsley had started brightly with Spaniard Diego Leon catching the eye, but for the second Championship game in a row, the Tykes struggled to convert their chances.
Coventry almost went two-up when big defender Elliott Ward struck the post with a firm far-post header.
Barnsley did manage to draw level a minute before the break when skipper Brian Howard slammed in a terrific left-foot shot from Gary Teale's cross from the right.
Coventry regained the advantage in the 68th minute when good work by keeper Kieron Westwood and the impressive Eastwood enabled Julian Gray to curl a delightful right-foot shot in off the far post.
Barnsley were denied a penalty by referee Steven Bratt following a handball appeal and the official then sent off the home side's livewire striker Iain Hume ten minutes from time for a second bookable offence.