The 19-year-old on loan Sunderland striker finished clinically in the fourth minute of a tight game to send the visitors crashing to their first defeat since Boxing Day.
Chesterfield had not won since they demolished Hereford at home in late January but once Dowson had put them in front, they gave Brentford few chances to strike back.
Peter Hartley also did well on his debut and Lloyd Kerry had an impressive home debut in the centre of midfield alongside Jamie Winter.
Brentford could not find the form that has taken them to the fringes of the play-offs under manager Andy Scott and they also lost their captain Matt Heywood in the second half.
The big centre-half was replaced by Darius Charles and the news from the dressing room was that he may have suffered a broken rib.
That would be a major blow to Brentford who also lost right-back Osei Sankofa with a foot injury at half time and Scott admitted his team could be without three players for Tuesday night's game at Accrington Stanley.
Brentford will need to show more invention if they are to rediscover the winning habit because they created little in what was a disjointed game, dominated to some extent by the strong winds.
The conditions were certainly a factor but it was Brentford's own sloppiness that allowed Dowson to score with his first touch.
Gary Smith carelessly lost possession and that allowed Jack Lester to turn away from his marker and send Dowson sprinting into the box to beat Ben Hamer with a well placed shot from 12 yards.
The visitors gradually found some rhythm but their best opening fell to Smith in the 25th minute and his low shot was kept out by the outstretched left leg of keeper Barry Roche.
The second half was a cagey affair with few chances at either end. Bees' Robert Milsom almost fashioned something for his team with a 69th minute free-kick that Alan Connell glanced just wide.
Lester was always a danger and he almost beat Hamer to a through ball near the end but the keeper got there just before him and that set up a nervous five minutes of stoppage time for the home side.
But for all their pressing, Brentford could not break down a determined Chesterfield defence and the home side deservedly held on to claim their first victory in seven games.