Chelsea’s new boss Rosenior watched his new charges from the stands at Craven Cottage.
The Englishman, who replaced the departed Enzo Maresca this week, will be in the dugout for the first time at second-tier Charlton in the FA Cup third round on Saturday.
The former Strasbourg boss said before kick-off that the team “need to hit the ground running for the rest of the season”.
But, still under the interim leadership of Calum McFarlane, they were reduced to 10 men midway through the first half when Marc Cucurella was shown a straight red card for hauling down Harry Wilson.
Liam Delap cancelled out Raul Jimenez’s opener but Wilson scored what proved to be the winner from the edge of the area.
Bournemouth beat troubled Tottenham 3-2, with Semenyo scoring from outside the area deep into stoppage time on his 26th birthday.
The winger, expected to join City over the next few days, was given a standing ovation when he was substituted moments before the final whistle.
Defeat heaps the pressure on Thomas Frank, who has overseen just two wins in his past 12 Premier League matches during his first season at the London club.
Brentford beat Sunderland 3-0 courtesy of two goals from Igor Thiago, who now has 16 Premier League goals this season, and one from Yehor Yarmolyuk.
The win lifts Brentford to fifth in the table.
Everton, reduced to nine men late in their match, held on to draw 1-1 with bottom club Wolves.
United travelled to relegation-threatened Burnley under the temporary leadership of former midfielder Darren Fletcher, two days after the sacking of Amorim.
Benjamin Sesko doubled his Premier League tally for the season, scoring twice as United came back from a goal down at Turf Moor.
But Jaidon Anthony finished smartly past the diving Senne Lammens as United drew 2-2, dropping more valuable points.
Harvey Barnes scored a dramatic winner in the 102nd minute as Newcastle beat Leeds 4-3 at St James’ Park.
The home fans chanted for former manager Kevin Keegan as the club posted the words “We’re all with you King Kev” on the big screen.
The club earlier shared a statement from Keegan’s family announcing the ex-England boss had been diagnosed with cancer.