QPR took the lead within the first two minutes when Hoilett beat Phil Neville to a loose ball on the edge of his own area and ran the length of the field to fire in via a deflection off Leighton Baines which wrong-footed Tim Howard.
Everton hit back shortly after the half-hour mark when Sylvain Distin headed a Steven Pienaar free-kick onto the post, with the ball rebounding onto the back of Julio Cesar and into the QPR net.
Any hopes the Toffees had of winning the game were diminished in the 61st minute when Pienaar was controversially shown a second yellow card for an alleged trip on Jose Bosingwa.
A draw, however, was a fair result from an entertaining afternoon in west London, but it leaves Mark Hughes' side still searching for their first Premier League win of the season.
The build-up to the match was dominated with speculation as to which players would boycott wearing t-shirts in the warm-up supporting the anti-racism 'Kick it Out' campaign.
Anton Ferdinand and team-mates Shaun Wright-Phillips and Hoilett opted not to wear the shirt, following the stance taken by Ferdinand's brother Rio prior to Manchester United's game against Stoke on Saturday and by Reading striker Jason Roberts.
QPR boss Mark Hughes would have been fully focused on the game, however, knowing a decent start from his side was a must having conceded early goals in their previous two outings. He was not to be disappointed.
Everton pressed in the opening couple of minutes but after having a second early corner cleared Neville lost possession to Hoilett.
The former Blackburn winger burst into the Everton half before striking an effort that beat Howard after taking a heavy deflection off Baines.
Hoilett came close to adding a second in the eighth minute as he closed down Howard, who slipped as he looked to clear the ball. The United States international just got enough on the ball and the resulting cross eluded the on-rushing Bobby Zamora.
The first real chance for the visitors came after 17 minutes as Nikica Jelavic curled a free-kick towards goal that was pushed away comfortably by Julio Cesar.
It was QPR who then came close from a set-piece of their own but Ryan Nelsen could only direct a header from Esteban Granero's free-kick wide of Howard's goal.
Everton's equalised in fortuitous circumstances at a time when they were struggling to create clear-cut opportunities.
Pienaar whipped in a deep free-kick that Distin headed onto the post with the rebound hitting a prone Cesar and nestling into the corner.
The Toffees took some momentum from their stroke of luck and could have had a penalty seconds after the re-start but referee Jonathan Moss waved away Jelavic's appeals after he went down following a Stephane Mbia challenge.
Phil Jagielka then struck the crossbar with the resulting corner as QPR started to show the defensive fragility which has plagued them during the early parts of the season.
After the initial shock of conceding the equaliser QPR finished the first half the strongest but could not test Howard before the interval.
QPR captain Park Ji-sung came close in the opening exchanges of the second half but he could not poke Samba Diakite's cross home due to the close attention of Jagielka.
Everton boss David Moyes was quick to introduce Steven Naismith from the bench in place of the largely ineffectual Victor Anichebe, who also decided not to wear the 'Kick It Out' shirt before the match, as he looked to get more support for lone striker Jelavic.
Although spaces began to appear on the pitch there was a distinct lack of creativity, with both sides guilty of conceding possession too cheaply.
Everton were reduced to 10 men with just over an hour gone when Pienaar received his second booking inside nine minutes, although he appeared to make minimal contact on Jose Bosingwa who looked to be heading to ground regardless.
Despite losing Pienaar, Everton were the side pushing for a winning goal.
Kevin Mirallas saw his effort headed behind by Mbia and Jagielka's header from the resulting corner was brilliantly kept out by Cesar before Hughes introduced Djibril Cisse, with Zamora the man to make way.
Nedum Onuoha was also brought on as QPR finally started to look like a team with a numerical advantage.
Following a string of corners the visitors had Howard to thank for keeping out Hoilett at full stretch, with Granero firing the rebound high and wide.
Referee Moss was unmoved as Everton full-back Seamus Coleman appeared to up-end Hoilett in the penalty area as the home side took complete control.
Hoilett was again foiled by Howard moments later as the former Manchester United goalkeeper flew to his right to tip a curling effort around the post.
Adel Taarabt also bent a free-kick just wide as Everton started to struggle with the continued pressure from their hosts.
Moyes took off Jelavic to replace him with the defensive-minded John Heitinga whilst Hughes was forced to replace the injured Nelsen with Ferdinand.
The break in play for the substitutions seemed to take some of the sting out of QPR's onslaught on Howard's goal but Cisse came close to grabbing an 89th-minute winner when he fired wide.