Sean Johnson made four saves for NYCFC, who is 4-0-1 over their last five matches.
Brandon Vazquez scored in the 74th minute for FC Cincinnati to end the club's scoreless streak at 558 regular-season minutes. It is the longest such stretch in the MLS this season.
FC Cincinnati is 0-3-3 over their last six games and were blanked in five straight matches prior to Saturday.
Przemyslaw Tyton had three saves for Cincinnati.
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NYCFC had a 16-14 edge in shots. Both clubs put five on target.
Ring was close to being offside in the 39th minute when he received a pass from fellow midfielder Gary Mackay-Steven and sent a right-footed shot past Tyton and into the left corner of the net. The play was reviewed and Ring was ruled to have been onside when he got the ball.
The goal was Ring's third of the season.
Timmerholm made it 2-0 in the 55th minute in a sequence that began with a corner kick. The ball caromed toward Tinnerholm, who unleashed a ferocious left-footed volley from near the edge of the box that found the right corner of the net.
The tally was the second of the season for the defender.
Vazquez ended Cincinnati's long scoring drought 19 minutes later. His right-footed shot was saved by Johnson and the ball caromed back to him and the forward sent a left-footed shot into the net for his first goal of the season.
Vazquez had a second goal disallowed in the 76th minute when he was obviously offside before beating Johnson.
Cincinnati had a solid chance to tie it in the 79th when defender Kendall Waston was in perfect position to deal with a corner kick but his point-blank header was saved by Johnson.
Mackay-Steven entered the contest in the 30th minute shortly after Maximiliano Moralez sustained an apparent right knee injury.
Tinnerholm the difference in NYCFC's 2-1 win over FC Cincinnati
Anton Tinnerholm's stunner proves to be the difference for NYCFC. Watch MLS on ESPN+.
Tinnerholm's superb shot doubles NYCFC's lead
Major League Soccer: Anton Tinnerholm (55') NYCFC 2-0 FC Cincinnati. Watch MLS on ESPN+.