The goalkeepers made important saves in a tight contest, with Courtney Brosnan denying Elisabeth Terland twice in the second half and Phallon Tullis-Joyce keeping out Ornella Vignola at the other end.
It was only the second time United had failed to score this season, having also drawn a blank against Chelsea.
United started brightly, forcing two corners inside the opening seven minutes, but Everton soon offered a threat of their own. Yuka Momiki fired narrowly wide from outside the box after 10 minutes, with Tullis-Joyce watching the effort closely.
Clear-cut chances remained scarce as both sides struggled to find a way through. Rosa van Gool was booked in the 26th minute, before Everton won their first corner two minutes later.
Ruby Mace impressed in Everton’s midfield, while United’s backline, led by Maya Le Tissier, stood firm whenever the hosts threatened.
Everton put together a good move five minutes before the break, with van Gool and Vignola combining before the latter tested Tullis-Joyce. Both sets of supporters kept the noise up, even as the first half ended without a goal.
Vignola threatened again five minutes after the restart, striking well from outside the penalty area and drawing another fine save from Tullis-Joyce.
Terland then tested Brosnan from just outside the left edge of the box as United searched for an opener.
Simi Awujo replaced Ella Toone in the 68th minute and was booked seconds later for a tackle on van Gool. Awujo quickly became involved in United’s attacking play too, firing just over the bar in the 74th minute.
Brosnan produced another good save to deny Terland two minutes later, keeping Everton level as the match entered its closing stages.
United introduced Lea Schüller and Jayde Riviere for Julia Zigiotti and Jessica Park in the 79th minute, before Noémie Mouchon replaced Momiki for Everton.
A nasty collision between van Gool and Riviere brought both teams’ physios onto the pitch in the 83rd minute.
Andrea Medina received a yellow card in added time, but neither side could find a winner as the contest finished goalless.
Everton XI: Brosnan (c), Blundell,Ishikawa, Layzell, Wheeler, van Gool, Kitagawa, Vignola, Momiki, Mace, Pacheco.
Subs used: Noémie Mouchon for Momiki (82′).
Manchester United XI: Tullis-Joyce, Sandberg, Le Tissier (c), Lundkvist, Medina, Ella Toone, Park, Terland, Zigiotti, Janssen, Miyazawa.
Subs used: Simi Awujo for Toone (68′); Lea Schüller for Zigiotti (79′); Jayde Riviere for Park (79′).
Yellow cards: Rosa van Gool (26′); Simi Awujo (68′), Andrea Medina (90+′).
Red cards: None.
