Everton have three games in hand on Paul McGuinness' side and require only four points to steal third spot in the closing stages of the season.
The Cottagers had the better of the opening exchanges and managed an effort in the first minute but Muamer Tankovic fired over the bar. The bright start almost resulted in an opening goal as Solomon Sambou struck a post in the 21st minute and Sutherland made a wonderful save to keep out Tankovic from the rebound.
Gradually, the Reds made headway and Jack Barmby was unlucky to see a goal disallowed for offside after Jack Rudge's shot rebounded off keeper Marek Rodak and into his path. Rodak then thwarted Donald Love as the visitors ended the first half in the ascendancy.
United continued to press but Mats Daehli and Rudge were denied by Rodak while Sutherland had to be alert to prevent Patrick Roberts from opening the scoring. The ever-dangerous Tankovic had a couple of chances while the best opportunity for an away winner fell to substitute James Wilson, who almost broke the deadlock.
Cauley Woodrow could have snatched the points late on but sent the ball spinning wide when charging down a Sutherland clearance and then clipped the woodwork with a deflected drive. A draw was a good result on the night but United's fate is very much in Everton's hands.
United starting details: Sutherland; Love, McNair, Grimshaw, Ioannou; Rudge, Pearson, Weir, A.Pereira, Daehli; Barmby. Subs: Evans, O'Hara, Wilson, Byrne, Rowley.