But Aidy Boothroyd's side, who have now won just one of their last 11 games, were denied an 11th away win of the season when Barnett struck four minutes into the second half.
The point was enough to move Albion into second place on goal difference, while Watford's share of the spoils has also kept alive their own automatic promotion hopes.
Despite the fact they could not hold on to the lead, it was a positive response from Watford to their shock 3-0 home defeat at the hands of Barnsley in midweek.
Albion will, however, view it as a two points lost - especially as they dominated the second half when a win would have moved the back to the top of the table.
Ishmael Miller wasted a match winning chance when he just had Richard Lee to beat in the 66th minute after a pass from Kevin Phillips only to be denied by the Watford goalkeeper.
Zoltan Gera whistled a shot just wide five minutes from time and, moments later, Roman Bednar should really have won the game only to fail to hit the target from six yards following a Chris Brunt cross.
Albion have been exposed at set pieces all season and Watford quickly cashed in on that weakness.
Jobi McAnuff delivered a left-wing corner that John Joe-O'Toole met with a powerful header close-range header.
Albion goalkeeper Dean Kiely did well to beat out that effort, but he was powerless when Bromby hammered home the loose ball from just two yards.
Watford knew their best threat was from set plays and they came agonisingly close to doubling their advantage from a 38th minute free-kick.
Once again McAnuff was the architect when his centre was met by Tamas Priskin, but this time Kiely was equal to the challenge as he turned away the Slovakian's header.
Ironically Albion's best chance to equalise in the first half came from a set piece of their own after Ishmael Miller had been fouled on the edge of the area by Danny Shittu in stoppage time.
Neil Clement beat goalkeeper Lee with his free-kick, but was frustrated by the woodwork as the ball crashed off the bar.
But that effort set the tone for the start of the second half and Albion were level four minutes after the re-start.
John Eustace fouled Robert Koren on the edge of the area and from the resulting free-kick, Gera delivered a pin-point cross that Barnett steered past Lee from six yards for his third goal since last summer's £3million move from Luton Town.
That was Albion's 103rd goal of the season, but a 104th proved beyond them.