Gianfranco Zola's side built on their 1-0 victory against Birmingham City in their opening fixture with a mightily impressive performance in front of their home fans.
It could have been a different story for Bournemouth, who went into half-time at 1-1 when Lewis Grabban cancelled out Gabriele Angella's opener.
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But the dismissal seemed to galvanise the home side rather than hinder their progress as Angella, Deeney and Lewis McGugan all scored within 13 second-half minutes.
Deeney notched again two minutes from time before he completed the drubbing from the penalty spot in injury time.
QPR were unable follow their victory over Sheffield Wednesday on the opening day as they were held to a 1-1 draw away to Huddersfield Town.
James Vaughan opened the scoring in the 34th minute but Junior Hoilett cancelled that goal out just three minutes later as the points were shared.
Fellow relegated side Reading also had to settle for a 1-1 draw away to Bolton Wanderers at The Reebok Stadium.
Darren Pratley put Dougie Freedman's side ahead but former Sheffield United striker Nick Blackman equalised from the penalty spot five minutes after half-time for Reading.
Ipswich Town earned their first three points of the season with a comprehensive 3-0 victory over Millwall at Portman Road.
All the goals came in the came second half, with Tommy Smith and Paul Anderson notching after a Shane Lowry own goal had put Mick McCarthy's side ahead.
Elsewhere, Darius Henderson's injury-time effort earned Nottingham Forest a 1-0 success away to Blackburn Rovers, while a 94th-minute Scott Wiseman own goal saw Barnsley suffer consecutive defeats as they lost 1-0 to Blackpool at Bloomfield Road.
Middlesbrough and Birmingham City were both 1-0 victors away to Charlton Athletic and Yeovil Town respectively.
And there were also away successes for Burnley and Derby County, the former beating Sheffield Wednesday 2-1 at Hillsborough, while the latter defeated Brighton and Hove Albion by the same score.