Summer signing Sanchez netted from close range in the 20th minute after Yaya Sanogo had bundled the ball past keeper Kasper Schmeichel.
However, the Gunners’ lead lasted less than two minutes before Argentine Ulloa climbed above Laurent Koscielny to head in.
Sanogo spurned a series of chances to give his side the lead in the second half, while Jamie Vardy went close for the home side after the break.
The result left Arsenal on five points after three Premier League games and seventh in the Premier League table.
Newly-promoted Leicester City, meanwhile, moved up to 15th with their second point of the season.
Here are some of the best pictures from Sunday’s late kick-off.
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