Munro and Rooney were both on the scoresheet at Palmerston
Inverness took a step closer to returning to the Scottish Premier League but they had to fight all the way against 10-man Queen of the South.
Willie McLaren put Queens ahead after 10 minutes when he cut inside to hit the ball past Ryan Esson.
Adam Rooney pulled the visitors level before the break and set up Grant Munro for the Highlanders' second.
Queens defender Bob Harris was red carded for his challenge on Jonny Hayes before Rooney scored again late on.
Terry Butcher's side are now two wins away from claiming the First Division title.
Ross Tokely headed a Paul Burns effort off the line after six minutes as Queens started strongly.
Manager Kenny Brannigan had moved McLaren from the left to the right and, after Rocco Quinn played a great ball through to the winger, he showed he could play on either side as he cut in to fire past Esson at the near post.
Queens keeper Scott Fox pulled off two terrific saves to deny Eric Odhiambo, the first with his feet after 21 minutes and then a great one-handed save two minutes later.
Stewart Kean then had a great chance to extend Queens' lead as he chased down a long ball from Harris but, after holding off his marker, he shot over.
On the half-hour mark, Fox made another one-handed save, this time to turn away a header from Rooney.
Rooney eventually got on the scoresheet four minutes before the break. Richie Foran sprinted away from the Queens defence and cut the ball across from the by-line for Rooney to fire into the net from inside the six-yard box.
Queens were up for it again after the restart, Quinn, Kean and McLaren all with chances.
Kean did have the ball in the net on the hour mark but the offside flag went up on the far side.
Munro received Rooney's pass to edge Inverness into the lead on 67 minutes.
With 18 minutes remaining, Harris challenged Hayes in front of the Queens dugout and, after treatment, both players got back to their feet and referee Charlie Richmond showed the defender a straight red card.
Inverness took advantage of the extra man with Rooney adding to his goal tally with two minutes left.
Queen of the South: Fox, McKenna, McAusland, Reid (Hamill 29), Harris, McLaren, Scally, Quinn, Burns, Kean (Weatherston 72), Holmes (O'Connor 78). Subs Not Used: Hutton, McParland.
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