By Chris Harris at Emirates Stadium
Alexis scored one goal and made another as Arsenal gave their fans three precious points for Christmas.
The Chilean striker is tasting festive football for the first time and he took centre stage with a virtuoso display that started with a missed penalty.
Alexis recovered from that setback to head in Kieran Gibbs' cross eight minutes before half-time, and his mazy run set up Tomas Rosicky for a second goal shortly after Olivier Giroud had been shown a straight red card.
Charlie Austin's spot-kick reduced the deficit 12 minutes from time and Arsenal had to withstand heavy late pressure from their London rivals, but the 10 men held on to climb back to sixth place in the Premier League.
They are two points off fourth-placed Southampton and a point behind West Ham United - their next two opponents.
Wenger will need the full depth of his squad to absorb five games in 14 days and he made two changes for the second game of that testing run.
Rosicky was handed his first start of the Premier League season after recovering from a thigh injury; Alex Oxlade-Chamberlain, nursing a slight groin problem, made way. There was a defensive reshuffle too with Nacho Monreal replacing Calum Chambers while Mathieu Debuchy shuffled across to a more familiar right-back role.
Boxing Day football is one of English sport's most revered traditions and it's one that has suited Arsenal - they went into this game with only one defeat in 17 Premier League games on December 26.
The omens weren't so good for QPR - they had failed to score in five of their last six visits to the Gunners and had lost all eight of their away games this season. That said, they did have the in-form Austin leading their attack.
The first half was played in teeming rain and just 35 seconds were needed for proof that Alexis was in the mood. Bringing down a lofted pass on the right flank with his thigh, the Chilean juggled extravagantly before delivering a teasing cross that almost reached Giroud.
Alexis usually has his feet up at this time of the year - it's his first taste of Christmas football - but he continued to be the centre of attention, winning - and missing - a penalty after eight minutes.
The decision was clear-cut - former Gunner Armand Traore whipped Alexis' legs away as they raced for a loose ball in the box. The spot-kick itself was rather meek, and Rob Green plunged to his left to parry before scooping the rebound away from danger.
Rosicky made a point of geeing up a crestfallen Alexis, and it took a while for the Chilean to regroup. When he did, a dazzling run took him past two defenders before a slide-rule pass nearly played in Danny Welbeck.
Giroud forced Green into a full-length dive to keep out a free-kick just before the half-hour mark, but there was nothing the former England No 1 could do to keep out Alexis' header eight minutes before the break.
It was the culmination of a flowing move that saw Welbeck find Santi Cazorla and the Spaniard make inroads before slipping the ball to Gibbs for an inch-perfect cross. Alexis had drifted away from Traore and found redemption from six yards.
Steven Caulker headed wide moments later as QPR finally recorded an attack of note, but Arsenal looked comfortable and capable of further goals.
The pattern of the first half continued at the start of the second half - Arsenal proactive, QPR reactive.
The home side almost opened up the visitors when a patient build-up suddenly quickened in pace and Debuchy fired in a low cross that nearly reached Alexis at the far post.
But the picture changed eight minutes into the second period when Giroud was sent off.
In pursuit of a ball over the top, Giroud was nudged in the back by Onouha as Green rushed out to clear the danger. Aggrieved, Giroud got up to remonstrate and was shown the red card after his head made contact with the QPR defender.
Now the onus was with QPR and their manager, Harry Redknapp, brought on two attacking players - Leroy Fer and Junior Hoilett.
Arsenal fans settled in for a rearguard action but, instead, they were treated to a fine breakaway goal. Alexis - yet again - was the architect with a slaloming run that took him past three QPR defenders. He found Rosicky and the Czech's first-time effort took a slight deflection on its way past Green.
The Gunners had breathing space, and in Alexis they had the perfect counter-attacking weapon. But QPR halved the deficit with 12 minutes left when Debuchy tripped Hoilett and Austin hammered the penalty down the centre.
Now Arsenal had to dig deep. With Bobby Zamora thrown into the mix, QPR threw crosses into the box. Per Mertesacker, Debuchy and company headed them away.
The defending was determined, and desperate at times, but the Gunners clung on.
The points were Arsenal's. The relief was palpable.
Referee: Martin Atkinson
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