The quarterback, signed in the offseason as a free agent, completed five of his six pass attempts for 45 yards on the drive and then left the game early with a thumb injury.
"On the first drive, I liked the tempo," Feeley said. "I wanted to finish the first quarter but with the injury I couldn't. I think we're getting better, which is what you want to do in the preseason. We hope to build on that and continue to improve. We're showing improvement. We're not where we want to be, but we're headed in the right direction."
Rams running back Steven Jackson participated in only the team's first series. He carried the ball four times for 20 yards.
"It felt good to get out there with the first unit, the starting offensive line and have us start to work on the chemistry and the tempo of the game," Jackson said. "It felt really good just to get my feet wet and get banged up a little bit."
St. Louis got the ball back quickly after defensive tackle Fred Robbins recovered a fumble on the Browns' second play following the touchdown.
"It felt good, just coming out and trying to improve from last week," Robbins said. "We did some good things last week, but we had a lot of little mistakes we had to clean up. That was our focus today, to come out and play hard, eliminate some of our mistakes and play our football."
Robbins' fumble recovery was the first of five turnovers the Rams grabbed on the night. St. Louis grabbed two turnovers on fumbled punt returns and interceptions by cornerback Quincy Butler and linebacker Bobby Carpenter.
Rams rookie quarterback Sam Bradford benefited from two of the Browns first quarter turnovers and helped turn those into two field goals from Brown, who missed the preseason-opening loss to the Minnesota Vikings, to give the Rams a 13-0 lead.
Bradford, the No. 1 overall draft pick, struggled in his second preseason game. He completed just six of 14 passes for 24 yards, though he was not sacked and did not turn the ball over despite the adverse weather conditions.
The Browns rallied with a Jake Delhomme 6-yard touchdown pass to tight end Ben Watson and a Phil Dawson field goal in the second quarter and trailed 13-10 at halftime. Then Cleveland went ahead 17-13 on Josh Cribbs' 15-yard touchdown pass from Seneca Wallace in the third quarter.
But the Browns turned the ball over three times from that point and Rams third-string quarterback Keith Null led St. Louis to two scoring drives in the fourth quarter that ended with field goals by Brown.
The Rams return to preseason action on Thursday night with a game in New England against the Patriots.
NOTES: Starting tight end Billy Bajema had four catches for 32 yards. … The Browns were 0-for-5 on third down in the first half. … Rookie tight end Michael Hoomanawanui had two receptions for 33 yards and also recovered a fumble on special teams. … Rookie defensive end Hall Davis was credited with 1.5 sacks. … Linebackers Larry Grant and Josh Hull both had forced fumbles. … Long-snapper Chris Massey recovered a fumble following a punt in the first quarter. … After Feeley completed five of his six pass attempts, Bradford and Null combined for nine completions on 28 attempts.