Jake Moody had a golden opportunity to allow San Francisco (5-1) to escape with a win, but he missed a 41-yard field goal attempt wide right with six seconds to play.
Jordan Mason had put the 49ers ahead 17-13 when he rushed for an 8-yard touchdown with 10:58 remaining. Hopkins made a 50-yard field goal just over seven minutes later to pull Cleveland (3-2) within one, and the Browns' defense followed by forcing a three-and-out to set up the game-winning drive.
The 49ers lost star running back Christian McCaffrey (oblique) and wide receiver Deebo Samuel (shoulder) to injuries. Without those weapons, Brock Purdy struggled, completing just 12 of 27 passes for 125 yards with a touchdown and an interception. He took his first regular-season loss as a starter, falling to 10-1.
Cleveland quarterback P.J. Walker had 192 yards and two interceptions on 18-for-34 passing while starting in place of Deshaun Watson (shoulder).
Jets 20, Eagles 14
Tony Adams picked off Jalen Hurts on the first play after the two-minute warning and Breece Hall scored from 8 yards out on the next play for New York, which overcame an 11-point deficit to stun previously unbeaten Philadelphia in East Rutherford, N.J.
The win was the Jets' first-ever against the Eagles, who won the first 12 meetings between the franchises. Zach Wilson completed a two-point conversion pass to Randall Cobb following Hall's TD. Wilson threw for 186 yards on 19-for-33 passing.
Eagles quarterback Jalen Hurts had 280 yards passing - including 131 to A.J. Brown - and one touchdown while getting picked off three times. Philadelphia (5-1) led 14-3 in the second quarter before three field goals from Greg Zuerlein pulled the Jets (3-3) within 14-12 late in the third.
Dolphins 42, Panthers 21
Tua Tagovailoa threw for three touchdowns after Miami fell behind by 14 points in a victory over Carolina in Miami Gardens, Fla.
The Dolphins (5-1) didn't score in the first quarter, but the NFL's highest-scoring team got rolling after that. Raheem Mostert, who ran for 115 yards on 17 carries, scored three touchdowns (two rushing, one receiving) and NFL receiving leader Tyreek Hill racked up 163 receiving yards with one touchdown on six receptions.
The Panthers (0-6) remain the only winless team in the NFL despite going to the second quarter with a 14-0 lead. Rookie Bryce Young threw for 217 yards and one touchdown on 23-for-38 passing. Chuba Hubbard rushed for 88 yards on 19 carries and Adam Thielen had 11 catches for 115 yards.
Ravens 24, Titans 16
Justin Tucker kicked six field goals and Baltimore held off a Tennessee rally in the second half to earn a win in London.
After making four field goals in the first half to help Baltimore (4-2) open up a 15-point lead at the break, Tucker converted from 20 and 36 yards out in the fourth quarter to restore a two-score advantage. That became vital when the Titans (2-4) got a 38-yard field goal from Nick Folk with 38 seconds remaining.
Lamar Jackson completed 21 of 30 passes for 223 yards and a touchdown with an interception. He also led the Ravens in rushing with 62 yards on 13 carries. Tennessee quarterback Ryan Tannehill completed 8 of 16 passes for 76 yards with an interception before leaving the game with an ankle injury.
Commanders 24, Falcons 16
Behind Sam Howell's three touchdown passes and key interceptions by Kendall Fuller and Benjamin St-Juste, visiting Washington earned a win over Atlanta.
Howell completed 14 of 23 passes for 151 yards, while Fuller added nine tackles in addition to his third-quarter pick. Terry McLaurin led the Commanders (3-3) in receptions (six) and yards (81). Running backs Brian Robinson and Antonio Gibson added scoring receptions.
Falcons quarterback Desmond Ridder passed for 307 yards and two touchdowns but threw three costly interceptions, including one in the end zone grabbed by St-Juste with 5:17 to play in the fourth quarter. Atlanta (3-3) has lost three of its past four games.
Vikings 19, Bears 13
Jordan Hicks recovered a fumble and took it 42 yards for a touchdown in addition to grabbing an interception as Minnesota held on to beat host Chicago.
Kirk Cousins completed 21 of 31 passes for 181 yards and a touchdown for Minnesota (2-4). Jordan Addison caught the Vikings' lone touchdown pass as Minnesota emerged on the positive end of its sixth consecutive game decided by eight points or fewer.
Justin Fields completed 6 of 10 passes for 58 yards and one interception for Chicago (1-5) before leaving in the third quarter because of a right hand injury. It was later reported that he dislocated his right thumb. Fields was replaced by undrafted rookie Tyson Bagent, who completed 10 of 14 passes for 83 yards but threw a costly interception in the final two minutes.
Texans 20, Saints 13
C.J. Stroud threw two touchdown passes and the Houston defense held New Orleans without a touchdown after the first quarter in the host Texans' victory.
Stroud threw the first interception of his rookie season, but he and the Texans (3-3) overcame that as he threw for 199 yards and hit Dalton Schultz and Robert Woods for first-half TDs.
Derek Carr passed for 353 yards and a touchdown, but New Orleans (3-3) was scoreless in three trips deep into Houston territory in the fourth quarter.