In the absence of the injured Olivier Giroud, close-season arrival Sanchez added to his crucial Champions League winner against Besiktas in mid-week with a 20th-minute opener for Arsene Wenger’s side.
But Ulloa responded with a header just two minutes later as Leicester maintained their unbeaten home league record and provided further evidence they can hold their own in the top flight.
They were more than good value for their point on what proved a frustrating afternoon for Wenger, whose side remain unbeaten on five points but lost ground at the top of the table.
Last weekend, Giroud’s late goal rescued a point against Everton, but with the France international absent for up to four months with a broken tibia, this performance raised concerns they will struggle for goals in his absence.
Yaya Sanogo, Giroud’s deputy, endured a forgettable afternoon that left him without a goal in his 17 competitive outings for the club.
And Arsenal supporters left Wenger in no doubt over their feelings as they chanted for him to sign a striker before Monday’s transfer deadline in the closing moments of a entertaining and even contest.
There was concern early on for Arsenal’s Laurent Koscielny when he bore the brunt of an ugly aerial collision with Jeff Schlupp.
Under new Premier League rules, the defender was forced to leave the pitch to be examined by a club doctor before returning with his head heavily strapped.
Wenger’s team had a fortuitous escape in the 18th minute when Riyad Mahrez’s neat one-two with Andy King culminated in a low drive that flashed inches past the post.
Arsenal claimed the lead two minutes later after Santi Cazorla outfoxed the Leicester defence with a dinked ball to Sanogo.
The French forward’s attempt lacked conviction, but to Arsenal’s good fortune, Kasper Schmeichel’s save served merely to divert the ball into the path of Sanchez, who swept home from close range.
– Ulloa hits back –
Leicester manager Nigel Pearson has instilled confidence in his team, however, and they drew level within two minutes, just as they had in their opening 2-2 draw with Everton.
A slick interchange between Schlupp and David Nugent on the left flank allowed the former to deliver an arcing cross from near the byline.
Fatally afforded time and space by Koscielny, Ulloa had the luxury of being able to pick his spot, planting a powerful header inside the left-hand post.
Less than four minutes later, Calum Chambers — fresh from receiving his first senior England call-up — was summoned from the bench to replace the struggling Koscielny.
Leicester began the second period as they had finished the first.
Ulloa should have put his team ahead after controlling Mahrez’s pass superbly and outwitting the sliding Chambers with a drop of the shoulder, only to clip his effort into the side-netting.
Cazorla, once more, broke the home side’s offside trap with a sublime scooped pass, yet the unmarked Aaron Ramsey headed tamely into Schmeichel’s arms.
Within a minute, a glorious opportunity came Sanogo’s way, with Nacho Monreal slipping him through down the inside-left channel, only for Schmeichel to step smartly off his line to thwart the Frenchman.
With his attackers labouring, it was no surprise to see Wenger make changes, with Sanogo and Cazorla replaced by Lukas Podolski and Alex Oxlade-Chamberlain for the final stages.
But for all of Arsenal’s possession, Leicester remained a major threat on the counter-attack.
The visitors had Szczesny to thank when he thwarted substitute Jamie Vardy following another incisive Leicester one-two, this time with Nugent.