It ensured United moved top of their Europa League group and will qualify for the knockout stages if they beat Partizan in the reverse fixture at Old Trafford on 7 November.
“We need to win away from home in the league, but another clean sheet and that gives you a platform to win games from,” said Solskjaer, whose team last won a Premier League away game in February at Crystal Palace.
Martial, making his first start since August, sent Vladimir Stojkovic the wrong way from 12 yards after United’s 19-year-old defender Brandon Williams won the spot-kick.
Williams’ burst forward to draw a foul from Nemanja Miletic was one of the the few bright spots in an otherwise uninspiring United display.
It helped Solskjaer’s team to their first win away from home in 11 attempts with their only shot on target.
Williams and 18-year-old midfielder James Garner were among seven changes made by United’s Norwegian boss from the side that started in the Premier League against Liverpool on Sunday.
And initially at least, United controlled possession, with Scott McTominay wastefully heading Juan Mata’s free-kick wide and Jesse Lingard’s curling effort striking the right-hand post.
However, the hosts carved out chances of their own with on-loan Roma forward Umar Sadiq bending a 20-yard strike against the post.
United keeper Sergio Romero superbly preserved the visitors’ lead by parrying Seydouba Soumah’s drive after the midfielder cut past Harry Maguire, as Solskjaer’s side hung on to record their first win on their travels since their Champions League victory over Paris St-Germain.
Possession without product
Solskjaer’s team arrived in Serbia on the back of the worst start to a domestic campaign for 33 years and having mustered just three goals in their last 540 minutes of competitive football.
While this was marginally better than their goalless Group L draw at AZ Alkmaar – in which they failed to register a single shot on target – there was still very little by way of invention.
United monopolised the ball early on but their possession brought few chances against a Partizan side sitting fifth in the Serbian SuperLiga.
Neither McTominay’s close-range header nor Lingard’s strike against the woodwork were a by-product of intricate, fast-paced attacking play – instead, the former came from a set-piece, the latter after a tackle by Aaron Wan-Bissaka.
Under Solskjaer, United it seems are arguably now geared more than ever towards counter-attacking, such are the limitations of his squad.
Recently described as a ‘quagmire of mediocrity’ by a member of staff at the club, those restrictions were particularly evident in midfield where Garner made his first start alongside McTominay and Lingard.
While Garner was neat and tidy, United’s midfield trio did little to address a familiar criticism among supporters – that the team simply does not possess the dynamism and creativity to breakdown perceived weaker opposition.
Wan-Bissaka and Mata struggled to deliver quality balls from the flanks, while Martial touched the ball just 18 times in his hour on the pitch, compared with Marcus Rashford managing 22 touches in a 30-minute cameo.
Partizan push United close
While Partizan trooped off the pitch defeated, applause nevertheless rang around the FK Partizan Stadium in appreciation of their efforts.
It was certainly a marked contrast to the side’s last two European home games, which were played behind closed doors after racist abuse by supporters.
“The crowd was unbelievable,” Solskjaer added. “I think the crowd should be very proud of their team and the team should be very proud of their crowd because it was an excellent atmosphere.
“You know what we talked about before the game… wow. the fans were great.”
At poignant venue for United – it was here that the Busby Babes lined up for the final time before the Munich air disaster in 1958 – Savo Milosevic’s team initially appeared in awe of the visitors.
However, as the game wore on, and with Solskjaer’s team increasingly giving possession away cheaply, Partizan pressed forward.
Sadiq caused Phil Jones and Maguire problems, while midfielder Bibras Natkho’s influence grew with Takuma Asano also seeing his late header saved by Romero.