By Josh James at Emirates Stadium
A brace from Alexis was enough to give us a much-needed three points.
After an enterprising opening half hour, the Chilean broke the deadlock with his 16th Premier League goal of the season.
Kieran Gibbs saw his low shot cleared off the line, but Alexis tucked home from close range, even if it did appear to bounce in off his hand.
Both sides had decent chances in an entertaining match, and Petr Cech denied Oumar Niasse in each half to preserve the lead.
The points weren't safe until virtually the last kick of the game. Alexis stroked home his penalty after Sam Clucas had handled Lucas's goalbound shot on the line.
It took his tally to 19 overall this season, and ensured the Gunners could put a troubled week behind them.
SETTING THE SCENE
Following back-to-back defeats, we came into the match against a resurgent Hull City under a certain amount of pressure.
Arsène Wenger made just one change to the team which lost at Chelsea last weekend. Kieran Gibbs replaced Nacho Monreal at left back, but the rest of the side was unchanged. That meant Hector Bellerin was passed fit after his head injury at Stamford Bridge.
Theo Walcott was in the starting XI too, needing just one goal to reach his century for the club.
There were plenty of attacking options among the subs too, with Lucas and Danny Welbeck returning to the squad, alongside Olivier Giroud on the bench. Mohamed Elneny was also in the squad after returning from the Africa Cup of Nations.
As for Hull City, Marco Silva - who won at Emirates Stadium as manager of Olympiacos last season - made two changes to the team that beat Liverpool last weekend.
This was his ninth match in charge of the Tigers, having won four of the previous eight to lift them up to 18th place, one point from safety.
We had been guilty of starting games slowly in recent times, but the team looked determined to show some attacking intent from the start in this lunchtime kick-off.
Alex Iwobi, Walcott and Mesut Ozil were moving the ball quickly up front, with Alexis breaking into the area at every opportunity.
But it was Bellerin who had the first real chance. He played a lovely give and go with Alex Oxlade-Chamberlain inside the box before flashing a shot just wide.
Alexis also saw an effort slip the wrong side of the post when well placed inside the area.
There were chances at both ends though. Niasse had a header at the far post clawed to safety by Cech after Kamil Grosicki found space on the left flank.
The Gunners continued to press, and Ozil volleyed over from an Alexis cross 12 yards out.
It eventually took the scrappiest of goals to break the deadlock. Gibbs smashed an effort goalbound from Ozil's cutback, only to see Andrew Robertson clear it off the line. Alexis was lurking in the right place though, and he bundled the ball over the line from close range, with the last touch seeming to be off his hand.
It came at a crucial time, just when Arsenal's early bluster looked to have blown itself out. The Gunners had mustered 10 shots on goal in the opening period, and overall we were good value for the lead.
Cech was needed early in the second period to preserve the lead, turning aside Niasse's shot when the striker was unmarked near the penalty spot.
Walcott was booked for his part in an altercation with Harry Maguire as temperatures briefly rose on a bitterly cold north-London afternoon.
Moments later Gibbs followed him into the book after hauling back the breaking Lazar Markovic. The two incidents brought the Emirates crowd to life, and Arsenal responded.
Iwobi fired over after swapping passes with Ozil and Oxlade-Chamberlain carried the ball 50 yards with a superb run down the left, but Hull got back in numbers to snuff out the threat.
It was open, often end-to-end stuff, with Hull looking dangerous down the right wing especially.
Welbeck and Lucas were introduced from the bench for the final 10 minutes, and it was the latter who won the last-minute penalty to seal the win.
His header at the far post was handled on the line by Clucas, who promptly received his marching orders. Up stepped Alexis to bury the spot-kick.
The Chilean had been instrumental in the build up to the penalty award, running onto a Ozil throughball, rounding the keeper outside the area then sending in his cross for Lucas from a narrow angle.
Penalty dispatched, job done.
Referee: Mark Clattenburg
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