But Campbell put Cowden back in front from the penalty spot only for Derek Holmes to level again for Queen's
Craig Reid saw red for the home side, but Campbell saw the resultant penalty saved and Cowden had Kenny Adamson and Colin Cameron red-carded late on.
Jimmy Nicholl's side opened the scoring after only 90 seconds when Campbell beat McKenzie with a low right-footed shot into the bottom corner.
Queens hit back and pulled level in 16 minutes thanks to Danny Carmichael's volley but, midway through the first half, Cowden edged back in front.
Campbell grabbed his second of the afternoon from the penalty spot after Ryan McGuffie tugged Mark Ramsay in the box.
Derek Holmes pulled the Doonhamers back level on the stroke of half-time when he latched on to a defensive error and hit a powerful shot past Ludovic Roy.
All the goals might have come in the first half, but the real drama came in the final 15 minutes.
Craig Reid was sent off for Queen's for stopping a clear goalscoring opportunity when he brought down Campbell.
However, McKenzie guessed right and saved Campbell's spot-kick denying the striker a hat-trick.
Then, with time ticking down, the visitors had Kenny Adamson and Colin Cameron red-carded after picking up second yellow cards, and they had to settle for a point as they battle to avoid a relegation play-off place.
Queen of South: McKenzie, Craig Reid, Lilley, Harris, Carmichael (McGowan 82), Burns, Johnston, McGuffie (Quinn 47), McLaren, Holmes, McMenamin. Subs Not Used: Hutton, McShane, Degnan.
Sent Off: Craig Reid (76).
Booked: McGuffie, McMenamin.
Goals: Carmichael 17, Holmes 45.
Cowdenbeath: Roy, Robertson, Winter, O'Brien, Adamson, Coult (McKenzie 77), Cameron, Ramsay, Linton, Campbell, Stewart (Crawford 72). Subs Not Used: Hay, Makel, Miller.
Sent Off: Adamson (84), Cameron (87).
Booked: Adamson, Cameron, Robertson.
Goals: Campbell 2, 31 pen.
Att: 1,102
Ref: Craig Charleston (Scotland)
Source: BBC Sport
Source: BBC Sport