The off-break bowler finished with figures of eight for 72 in 21.2 overs to hand the visitors a resounding win shortly after the halfway stage on the final day of the game.
Harmer, whose previous best figures were six for 55, ended with match figures of 11 for 149, with the home side showing little fight in their bid to chase down the 293 victory target.
Dane Vilas made 57 off 67 balls, including five sixes, before he was the last man out.
The win was a second in succession for the Warriors and lifted them off the bottom of the table, ahead of the Sunfoil Dolphins.
Most of their work was done in the morning session when the home side were reduced to 75 for five.
After the break, Justin Kemp and Vilas showed some spirit as they took the Cobras past 100 in the 47th over.
The two put on 45 together for the sixth wicket, but then saw the partnership broken when Harmer trapped the captain leg before wicket for 22.
Three balls later and in the same over Robin Peterson was caught at slip by Arno Jacob for a duck, while Rory Kleinveldt was caught in front lbw, also for a duck in Harmer’s next over.
All the while, Vilas was watching things go all wrong from the other end, but managed to get to his 50 in 62 balls.
A mix-up with Johann Louw (one) then saw the Cobras bowler run out by Kelly Smuts, with Vilas last man out when he found Lyall Meyer off Harmer handing the Warriors a convincing win.
Earlier, the Cobras resumed on 20 for none overnight with Andrew Puttick adding just four to his overnight score before he was first out when he edged Andrew Birch to Athenkosi Dyili for 19.
Yaseen Vallie, the other opener, added 25 with Stiaan van Zyl to take their side past 50 in the 18th over.
Disaster then struck for the home side with Vallie stumped by Dyili off Harmer for 18, followed by the dismissal of Justin Ontong for a duck two balls later to leave the score on 50 for three.
JP Duminy put on 10 with Van Zyl before he was caught by Jacobs for seven, Harmer again the bowler.
And the same two men combined to send Van Zyl on his way for 20 on the stroke of lunch.
That left captain Kemp and Vilas battling at lunch with their side in a massive hole, one that proved too deep to escape from as they suffered their first loss of the campaign.