With the Welsh side battling to preserve their league status and an Arctic gale enveloping Griffin Park, it was no surprise that the initial fare was less than pleasing on the eye.
Indeed, it took 15 minutes for the first significant action to take place when Glenn Poole's deep left-wing cross was met by Shakes at the far post, but the winger skied a volley over from 12 yards when he was left totally unmarked.
The home side continued to show the greater attacking intent and were rewarded for their efforts in the 31st minute when Shakes made up for his earlier miss.
Nathan Elder found Shakes in space in the Wrexham penalty area and the ball broke to Alan Connell whose effort was saved by Gavin Ward, but the keeper was helpless to prevent Shakes nodding home from close range.
Wrexham went close to drawing level moments later in bizarre circumstances. Simon Spender's hopeful punt upfield caught on the wind and was misjudged by Brentford goalkeeper Simon Brown, who was lucky to see the crossbar come to his rescue.
More uncertain goalkeeping by Brown followed when he was beaten to the punch by Phil Bolland following Danny Sonner's free-kick, but the defender's header landed on the roof of the unguarded net.
The second half commenced with snow falling from the sky, but the unseasonable conditions failed to prevent Wrexham from pursuing an equaliser which they nearly got when Neil Roberts got on the end of Spender's cross, only for Brown to smother his effort with an instinctive reflex save.
Brown preserved Brentford's lead again with 15 minutes remaining with a fantastic reflex save when Michael Proctor span and fired in a shot from eight yards which the goalkeeper managed to beat away.
And that miss proved costly when Shakes thundered home Elder's cross with ten minutes to go to seal the win for the London side.