First-half strikes from Beth Lumsden and Shania Hayles were enough for United to pick up all three points in front of a 3,221-strong crowd.
Becky Langley could not have asked for a better start from her side when Lumsden found the back of the net after just five minutes.
Hayles managed to wriggle free from her marker and lofted a cross towards the back post, where Lumsden pulled off a fantastic acrobatic volley to register her first of the season.
United continued to press the Blades in their final third and almost doubled their lead 12 minutes after the opening goal. Goalscorer Lumsden pinched the ball and played in Hayles, who saw her effort held well by Sian Rogers from close range.
Hayles' pace continued to cause havoc up front as she breezed past Satara Murray just after the half-hour mark and opted to go for goal but dragged her effort wide of Rogers' far post.
Newcastle were relentless in their quest for a second goal, which duly arrived in the 41st minute when Hayles made it two in two games.
A Lois Joel cross to the near post was bravely attacked by United's number seven and powered past Rogers before she even had time to react.
Despite United dominating the first half, it was the Blades who came out of the blocks firing in the second 45 minutes. Just three minutes after the restart, a deep corner found its way to Leanne Conway at the back post who cannoned a half-volley off the crossbar.
The game began to open up in the second-half with Lumsden seeing a long-range half-volley whistle wide of the post before Maria Farrugia stormed through on goal but was thwarted by the onrushing Claudia Moan.
As the game entered the final 20 minutes, Sheffield United Women continued to throw players forward in search of a route back into the game and almost found one when Ellen Molloy was slipped in behind the United backline but was thwarted by Moan's smart save down low.
After coming off the bench, former Sheffield United Women player Sophie Haywood almost wrapped things up with three minutes remaining. Andrews drove into the box and unselfishly squared the ball to the number 18 but despite the ball being seemingly destined for the far corner, Rogers clawed the ball away at the last second.
Newcastle United Women: Claudia Moan, Lois Joel (Liv Watt 76), Deanna Cooper, Charlotte Potts (Hannah Greenwood 67), Demi Stokes, Elysia Boddy, Amber-Keegan Stobbs (Rachel Furness 76), Jasmine McQuade, Beth Lumsden (Katie Barker 85), Amy Andrews, Shania Hayles (Sophie Haywood 67)
Subs not used: Hannah Hawkins, Georgia Gibson, Kacie Elson, Isabella Sibley