Ole Gunnar Solskjaer put his faith in Greenwood, Angel Gomes and Tahith Chong, the trio's inclusion contributing to United's youngest XI in a Europa League or Champions League game since December 2012.
Yet with Marcus Rashford particularly inefficient in front of goal, the Premier League giants struggled to find a way to beat Astana goalkeeper Nenad Eric, who was in excellent form.
The hosts did at least claim victory. With 17 minutes to go at Old Trafford, Greenwood had the crowd off their feet with a stirring run and finish through Eric's legs to win the Group L game.
United's young side made a vibrant start with Fred's 30-yard strike rattling the crossbar before Rashford somehow hit a close-range shot straight at Eric.
Greenwood rifled a powerful drive wide and Rashford sprung Astana's offside trap again in the 21st minute but again found Eric blocking his way when it looked easier to score.
The 17-year-old Greenwood and Chong both arrived moments too late to convert Marcos Rojo's low cross as United tried to step up the tempo at the start of the second half.
2 - Manchester United have recorded back-to-back wins across all competitions for the first time since March 2019 (a run of three, featuring their victory at Paris Saint-Germain). Relief. pic.twitter.com/RbMq7L8Od1— OptaJoe (@OptaJoe) September 19, 2019
A goalmouth melee saw the ball roll against the outside of Eric's left-hand post before Rashford thumped a free-kick just over the crossbar and Fred's 25-yard set piece was tipped wide.
Eric brilliantly tipped Jesse Lingard's speculative strike on to the woodwork with Diogo Dalot failing to convert the rebound, leaving Greenwood's moment of magic decisive.
What does it mean? You can't win anything with kids… or can you?
Solskjaer's decision to name such an inexperienced front line was partly forced on him by Romelu Lukaku and Alexis Sanchez departing for Inter with no arrivals signed to replace them.
The virtually anonymous Chong and Gomes do not look ready to make match-winning contributions on this stage, although Greenwood certainly justified his inclusion with the winner.
A star is born
There has been a great deal of excitement around the potential of Greenwood, who was handed his second start for the club. For much of the game Greenwood operated on the fringes but he burst into life when it counted to ensure United avoided an embarrassing result.
Rashford wasteful as attack's leader
Easily the most experienced United attacker on show, Rashford could have had a hat-trick had his radar been in tune. He has only scored once since the opening weekend.
Solskjaer's side go to West Ham United in the Premier League on Sunday, with their next Europa League fixture away to AZ on October 3, the day Astana host Partizan.