Home supporters were in buoyant mood ahead of the first game of the English top-flight campaign, with four new signings unveiled on the pitch and new faces in the United boardroom also in attendance.
Just as they did at home for much of last season, however, United struggled to break down their opponent in the first half, with captain Bruno Fernandes going closest to breaking the deadlock.
Frustrations grew after the break as it looked like a winner would elude the hosts, only for substitute Zirkzee to arrive right on cue three minutes from time to give United the three points.
Zirkzee, who joined from Bologna for a reported $US47 million ($A70m) last month, was one of three off-season signings to make their first appearances for United, along with defenders Noussair Mazraoui and Matthijs de Ligt.
"To win here in my first home game, and to grab a goal, it couldn't be better," Zirkzee said.
Zirkzee, Mazraoui and De Ligt have arrived as part of a $US180m ($A270m) spending spree by the record 20-time champions, a club under new leadership and looking to return to its former glories.
Erik ten Hag was retained as manager despite guiding United to an eighth-place finish last season and this was a solid, if unspectacular, start to the campaign by his team.
With Zirkzee not fully match sharp and Rasmus Hojlund injured, United started the season without an out-and-out striker on the field and it showed, with midfielders Fernandes and Mason Mount wasting the best opportunities in a game that was petering out before Zirkzee's late intervention.
Fulham goalkeeper Bernd Leno came to his team's rescue, saving twice at the feet of Fernandes in one-on-one chances then getting down sharply to deny Mount from close range in the second half.
Leno had no chance with Zirkzee's shot in front of the Stretford End, however, and Garnacho squandered a great chance to make it 2-0 in stoppage time when he dragged a shot wide in front of an empty goal.
Mazraoui played 81 minutes at right back before being replaced by De Ligt, three days after they both joined from Bayern Munich. Zirkzee entered in the 61st.
with AP
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