The Gunners head into the fixture sitting in sixth place in the Premier League and know taking all three points off the Cherries would mean they would be third going into the global break.
Jack Stacey forced Bernd Leno into his first meaningful action of the afternoon as the Germany goalkeeper had to tip a cross-cum-shot behind for a corner.
The 30-year-old Gabon worldwide has made an impressive start to the season, scoring seven goals in eight league appearances.
Substitute Joe Willock fed Martinelli, who shot wide, but Arsenal could have conceded a penalty as Wilson was barged over by Kolasinac.
Bournemouth came out after the interval seemingly much more up for the fight and came close to levelling as Callum Wilson showed neat footwork before squaring across an open goal, only for Calum Chambers to clear away under pressure.
"I can not believe this Arsenal team are third in the table". Though given the home side's advantage in the first half, it should have been a lot simpler.
"I'm critical of the team but also very positive".
"We knew if we won we could go third and that was important for our confidence", Emery said. For me it's one step more for the young players, for us.
Bournemouth, who were beaten 5-1 on their last trip to the Emirates Stadium, produced a cagey display in the first period, although they almost equalised when Dominic Solanke narrowly missed the target with a header from a free kick.
"We could have scored more in the first half, but we controlled the game". They created some chances, we created some chances and it's always like that.
"We dominated possession and deserved a point, we did well enough and had good enough chances".