It was a tough night for Newcastle on Monday as they saw little of the ball and spent a lot of the time chasing it unsuccessfully against their dominant opponents.
The visitors only had one shot on target in the opening 45 minutes, when Rondon proved too strong for Sokratis but saw his low strike pushed wide by Leno.
Even though Arsenal central defender Shkodran Mustafi looked a weak link as he repeatedly lost the ball, Newcastle struggled to create chances.
Indeed, they did not have a shot on target after the break with Ki Sung-yueng shooting wastefully wide from the edge of the area in a rare opportunity to equalise, before Lacazette sealed the three points for the home side in the 83rd minute.
After their 2-2 draw at Bournemouth on 16 March, Magpies' boss Rafael Benitez said Newcastle needed one more win to secure their Premier League status and they have six games left to do that.
However, they are seven points clear of 18th-placed Cardiff and still have to play three of the six teams below them - Southampton, Brighton and Fulham - so it would be a major surprise if they dropped into the Championship.
Former Blackburn striker Chris Sutton on BBC Radio 5 Live
Arsenal were really, really impressive. They have been flying at the Emirates all season. When you think about it, the top four looked too far away at the start of the season but it's in their hands now, although five of the last seven [games] are away for them.
They limited Newcastle to very few chances. You feel Arsenal fans are right behind Emery. In some ways they are overachieving this season.