Lowe opened the scoring in the fourth minute before two fine saves from Owain Fon Williams prevented the Sky Bet League One's top scorer Callum Wilson from levelling.
Jake Kirby capitalised on poor defending to make it two after 37 minutes and Lowe lobbed in a third just before half-time.
Lowe completed his hat-trick in the 53rd minute with a super strike from 35 yards.
Carl Baker pulled one back from the penalty spot - after Danny Holmes had handled - and Ash Taylor was sent off for a high challenge.
But James Wallace capped a great day for Rovers with a powerful drive to mark his first appearance since December.
Moore said: "It was fantastic. We had worked on our closing down and the squeezing and keeping the ball and some of our finishing was first-class.
"Ryan Lowe has shown what a player he is. His hat-trick goal was fantastic.
"The changing point in the game is the two good saves that Owain Fon Williams made very early on.
"When Wilson got in, he twice made a great save and if that goes in it's a different game. Goals change games.
"I was disappointed with the sending off.
"I think the referee probably over-reacted with the crowd.
"Ash Taylor had got to clear that and the lad has put his head down and he's ended up kicking him and at worst it is probably yellow card.
"I thought the penalty was harsh. If someone had offered me a draw I would have taken that and not come, so to come away with the three points was fantastic."
Rovers are unbeaten in six, while Steven Pressley's Coventry lost for the first time since September.
Pressley said: "I'm not going to be overly critical of this group of players because their performances this season have been top-level.
"What this proved to us was that if we don't play with that intensity and don't press the game in the cohesive manner that we work towards then we are maybe not the team we like to think we are.
"There is still a lot of work to be done. The one thing that this game tells us is exactly that.
"If we start believing that we are better than we are then we have a problem. This was a stark reminder of that for us.
"The key word for me was intensity. We didn't play with that intensity.
"We can't keep losing five, four or three goals. We have to tighten up in those areas, but there were several reasons for that and we have to ensure that doesn't happen again."
- Sports & Recreation
- Owain Fon Williams
- Ryan Lowe
- Callum Wilson
- Ash Taylor