Arsenal fell behind just after the hour mark as Mane's left-wing cross was tipped away by Leno into the path of Milner, and the midfielder composed himself to drill into the net from 15 yards for his 50th Premier League goal.
On Friday, the Spanish manager admitted he wants to address Arsenal's awful record against the Premier League's top six by beating the Reds.
The first half was played at breakneck speed with several chances for both sides.
It is worth noting that Bournemouth have had things relatively easy up to this point; both of their matches against one of last season's top seven have resulted in their two defeats of the campaign, and more hard tests are to come with Saturday's match marking the beginning of a six-game streak during which time they will face United, Arsenal, Manchester City and Liverpool.
Emery said the early defeats still play on his mind as he prepares his team for the visit of Jurgen Klopp's Liverpool. "Maybe their dropped points at Crystal Palace last weekend will have sharpened minds".
"The result tomorrow is important but first I want to show everyone our best mentality in the game". We need more, in our work and tactically also. "I think this is the day Arsenal show some big cracks".
The teams' Premier League seasons so far.
Where to from here for asylum seekers?
Hundreds of children have been moved from Nauru to Australia for treatment in the past few years, accompanied by their families. Today , he claimed criticism of poor living conditions among the would-be asylum seekers was offensive to the people of Nauru.
Lacazette shot wide from an acute angle before turning home Mustafi's header across goal, only to see the goal correctly ruled out as the Germany defender was clearly offside.
Alexandre Lacazette struck a late equaliser through Alex Iwobi's pass, as Arsenal and Liverpool shared the spoils in an entertaining Premier League clash.
Nacho Monreal is facing a race against time to prove his fitness but Sead Kolasinac is back in full training after recovering from a hamstring injury so he should be passed fit to return at left-back. City have recorded 7 clean sheets out of 10 matches played so far this campaign, only conceding one goal apiece in the games that they have conceded, although these matches still ended in victory.
'If you enjoy it as a spectacle then it is good!
When they have faced quality opposition, Liverpool have usually let goals in. In their last nine league games, Gunners have scored at least two goals in each of them. They are also likely to miss the Champions League trip to Red Star Belgrade on Tuesday.
Arsenal will be looking to close-in on the top two with a win when Liverpool arrive at the Emirates on Saturday evening.