Jose Sosa opened the scoring for the Black Eagles on 16 minutes with a brilliant free-kick effort taking his tally for the season up to 7 goals and 10 assists this season.
Rizespor could have equalised four minutes later but Deniz Kadah missed from the penalty spot.
The home side were punished soon after when former Arsenal youth Oguzhan Ozyakup setup ex Fulham youngster Kerim Frei for the Eagles second goal.
Frei now has 5 goals and 3 assists in 1,133 minutes this season which is a better ratio that the two wingers currently ahead of him in the pecking order.
First-choice winger’s Olcay Sahan and Quaresma have 3 goals, 5 assists in 1,848 minutes and 4 goals, 6 assists in 1,900 minutes, respectively.
After rising through the youth ranks at Fulham Frei was given his Premier League debut on 10 December 2011, in an away match against Swansea City aged just 18.
The Turkish international joined Beşiktaş on a €3.5 million move from Fulham in 2014.
Ozyakup now has seven goals and seven assists in all competitions for the Istanbul giants this season.
The 23-year-old midfielder joined the Eagles from Arsenal in 2012 and has gone onto establish himself as one of the brightest talents in the league.
The Turkish international midfielder is currently the third highest – statistically – rated player in the Turkish league with a 7.44 average score.