In the first league meeting between the two sides, a controversial second-half penalty from Charlie Austin consolidated Rangers' position as the league's early pacesetters - and condemned Yeovil to a fifth successive defeat on home soil.
Harry Redknapp's side, who recorded their sixth consecutive clean sheet in all competitions, could have taken an early lead when summer signing Matt Phillips ran through on goal, only to poke the ball tamely wide of the target.
However, despite Rangers' starting line-up boasting an abundance of Premier League experience, it was the Somerset side that impressed during a tight opening period.
Yeovil - who have now only scored three goals in eight league matches - grew in composure as the half developed with lone striker Andy Williams stretching defensive duo Richard Dunne and Clint Hill.
In contrast, high-flying QPR struggled to offer Austin any service during a disappointing first half - with the lone striker's frustrations landing him in referee Gavin Ward's notebook after a rash tackle on Glovers defender Luke Ayling.
Yeovil continued to impress and came close to breaking the deadlock when Joel Grant forced goalkeeper Rob Green into a smart low save.
The hosts then saw Joe Ralls and Joe Edwards both spurn good openings, before Green spared QPR's blushes before the break with a terrific sprawling save to keep out Liam Davis' low drive.
QPR started the second half slowly and gave a capacity Huish Park crowd belief that their side could pick up a surprise first league success since a last-gasp win at Millwall on the opening day of the season.
But the home side - who are still yet to score a home league goal this campaign- struggled to make their dominance count and wasted a number of clear-cut chances.
Green was at the centre of the action at the beginning of the second half, producing an outstanding double save to deny Ralls and Davis.
But moments later, Austin sprung into life and saw his right foot shot creep agonisingly wide of Wayne Hennessey's post.
Redknapp brought on Shaun Wright-Phillips and Niko Kranjcar to inject some urgency into his side - but it was stopper Green who continued to impress after clawing away a fierce Williams strike.
However, Yeovil paid the ultimate price on 75 minutes when Austin scored his third goal of the season with a clinical spot-kick, after Dan Seaborne was adjudged to have impeded the former Burnley man.
The home side poured forward looking for a late reprieve - but the visitors' defence held firm to earn their fifth 1-0 league win of the campaign.