M'Baye Niang's stunning early strike put Watford in front at Vicarage Road before Deeney doubled his side's advantage with a scruffy finish soon after half-time.
Hornets defender Miguel Britos was shown a second yellow card for bringing down Salomon Rondon with 25 minutes left but the hosts held on to register back-to-back league victories for only the third time this season.
The result means Watford sit seven points behind eighth-placed West Brom in the table, although the Baggies have played one game fewer.
Perhaps more importantly, Walter Mazzarri's men are now 10 points clear of the relegation zone and while yet to reach the hallowed 40-point mark, they can realistically start planning for a third consecutive season in the top flight.
Both these sides appear to have played in fits and starts this term and the outcome could have been very different had Nacer Chadli given West Brom an early lead.
The Belgian's first finish, however, was blocked by Watford goalkeeper Heurelho Gomes and as the ball spun up he failed to guide the volley into the open net from an acute angle.
It proved a costly miss because in the 13th minute the Hornets took the lead. Deeney's flick-on ended up at the feet of Niang, who drifted in-field off the left before unleashing a stinging shot past Ben Foster and into the far corner.
West Brom spent most of the next 20 minutes chasing shadows but Chadli almost equalised when his bending free-kick from 30 yards clipped the outside of the post.
Tempers frayed at the end of the first period and a frustrated James McClean was fortunate to escape with only a yellow card when he kicked out at Jose Holebas.
Read the full article on eurosport.co.uk: Deeney scores 100th goal for Watford in win over West Brom