Mkhitaryan poor, Iwobi good, Leno strong, Kolasinac redeemed
Mkhitaryan is a sound player technically. However, he didn't impress at Manchester United, and he hasn't thus far at Arsenal.

Versus Bournemouth, he did try to utilise the ball, but his end product wasn't forthcoming. This has been apparent for months now, and he really needs to step it up.
Iwobi, in contrast, was very good and did provide in the final third. He ensured Kolasinac had a pass to make to Aubameyang for the winner, and he linked up well with the wide men and Aubameyang to create openings in both halves. Iwobi has enhanced this season and looks bulkier than before. If he sustains this over the long-term, he can be a world class player. It may seem like hype, but he has begun to fulfill his long-term potential.

Bernd Leno was strong in this game and has been since he took Cech's starting place. He has looked very assured, strong in the air, and is a capable handler. He can be an asset for both Arsenal and Germany for years to come.

Kolasinac, however, redeemed his poor performance vs. Wolves, and was instrumental in providing Arsenal's width today. He is an adept wing-back, due to his pace, strength, tenacity, and crossing ability. He had a strong hand in both goals, and one must hope that his poor game vs. Wolves was an anomaly.

Overall, Arsenal didn't perform to their optimum at Bournemouth, but it was a professional win nonetheless. With the next league game against Spurs, and their stellar win over Chelsea, the first North London Derby of the season will be a closely contested game. Both sides have players who can cause major damage to the other, and it will be battle in various areas.
But for this game, Arsenal did was needed to be done, and were worthy winners, ultimately.