Reading were also reduced to 10 men when Ivar Ingimarsson was sent off moments into the second half, but by then Rangers were 2-0 up and cruising.
The hosts have scored 13 goals in their last three games at Loftus Road - while Reading have managed 11 all season and are now three points off the foot of the table.
They pulled one back at the death through Brian Howard, but the damage had long been done and the disgruntled travelling support treated Rodgers to a chorus of 'you're getting sacked in the morning' and chanted former boss Steve Coppell's name.
Reading's nerves in front of goal were illustrated when Jimmy Kebe blasted high over the crossbar early on.
Rangers, by contrast, are brimming with confidence and Adel Taarabt's de turn and shot forced a fine save from Adam Federici.
The game exploded into life on the half-hour when Watson, already on a yellow card after a clumsy foul on Shane Long, was sent off by referee Andy Hall for taking a free-kick too quickly.
But the official appeared to have done Rangers a favour after the on-loan Wigan midfielder had trudged off, as Buzsaky stepped up to take the same free-kick and hit a superb curler past Federici and into the corner.
The 10 men doubled their lead eight minutes later when Wayne Routledge floated in a deep cross which fooled Federici and allowed Simpson to volley into the net at the far post.
The luckless Royals came within inches of pulling one back at the break but Simon Church thumped his free-kick against the post.
Hall evened up the numbers less than 30 seconds into the second half, although he had little choice after Ingimarsson, also on a booking, scythed down Simpson.
Substitute Vine squandered two gilt-edged chances in as many minutes and also had a goal disallowed for offside, but the striker eventually registered his first goal of the season with a cool near-post finish.
And fellow sub Agyemang raced onto Gavin Mahon's pass and rounded Federici to break his duck this campaign.
Howard finally gave the away fans something to shout about with a consolation goal, but that only prompted one Royals supporter to race onto the pitch towards home keeper Radek Cerny to round off a rotten evening for the visitors.