Mkhitaryan moved to the Italian capital on a season-long loan on the final day of the European transfer window. The Armenia international made a goalscoring start to his career in Serie A, helping Roma beat Sassuolo 4-2 on Sunday.
Dzeko also got on the scoresheet and was left suitably impressed by the new man's contribution, per Metro: "He's a great pro. I remember him also from Borussia Dortmund times and he will be a big player for us. Hopefully, he can stay a long time here. He will see that we are playing football here and immediately he scored a goal so hopefully, he can have more goals and a lot of assists for us."
Mkhitaryan had already offered Dzeko a hint of what was to come by scoring twice as Armenia beat Bosnia and Herzegovina 4-2. Dzeko revealed he told Mkhitaryan after the game, "my friend, next games you have to score for Roma as well!"
Mkhitaryan duly obliged and already looks like a different player to the one who left the Gunners. The 30-year-old struggled mightily in north London after arriving from Manchester United in the winter of 2018.
However, Mkhitaryan's confidence and performances appeared to wane soon after. Wenger was replaced by Unai Emery in the summer of 2018, and Mkhitaryan struggled to earn regular playing time.
A return of six goals and seven assists in all competitions last season wasn't bad, but Mkhitaryan made just 19 starts in the Premier League. Alex Iwobi was often preferred to the former Borussia Dortmund and Shakhtar Donetsk star.
Mkhitaryan said he knew he "was not going to play a lot" with the Gunners this season, per Simon Collings of the London Evening Standard. The feeling prompted his desire to move, with Roma sporting director Gianluca Petrachi recently saying Mkhitaryan "has given up on lots of money to come to Rome," per the Daily Star's Callum Vurley.
One goal won't make Mkhitaryan's Italian adventure a success, but if his confidence returns, he has the core vision, pace and finishing ability to be a consistent match-winner for Paulo Fonseca's team.
If that happens, Roma may be encouraged to make the deal permanent, especially since Mkhitaryan's chances of returning to Arsenal and making the grade look slim. The Gunners signed winger Nicolas Pepe from Lille in a club-record transfer this summer and took Dani Ceballos on loan from Real Madrid.
Head coach Unai Emery has also been keen to give playing time to promising academy graduates Joe Willock and Reiss Nelson. With Mesut Ozil still in the fold, Arsenal remain well-stocked in the attacking areas of midfield and could afford to cash in on a high-earner who doesn't appear to be part of the club's plans moving forward.