County strolled to victory against a weakened Jags side to set up a tricky second-round North Cup home tie against title-chasing Brora Rangers.
Nairn manager Ronnie Sharp said: “It was a fairly comfortable win and we weren’t really put under too much pressure by Strathspey.
“We bossed the game from the start and although our finishing wasn’t clinical we did more than enough to win comfortably.
“We also manager to keep a clean-sheet into the bargain.”
Strathspey manager Brian Grant was forced to bring on back-up goalkeeper Stewart Black in attack for the last half hour due to lack of numbers on the bench.
Grant said: “I would have been very surprised if Nairn hadn’t won given the players we had to pick from – we just didn’t have a team at all.
“There has been a lack of commitment from our players this season.
“It has got to be addressed at some point soon and quite a few players are set to move on in the summer when we will try to change things around.”
The visitors took the lead in the fifth minute, Jordan Macrae beating Michael MacCallum with a header, and it was 2-0 in the 28th minute, Gary Kerr nodding home.
Wayne Mackintosh made it 3-0 from the spot in the 53rd minute after Jack Maclean had been brought down in the box and Kerr completed the scoring three minutes later with another header to cap a frustrating day for Strathspey.