Salisbury took a point home after Robbie Gallagher's opener in Essex, but felt they could have taken all three after a late onslaught on the Chelmsford net.
It took some time for the fixture to come to life, but the Whites had the upper hand in possession and looked the more threatening side.
The hosts had a shot well off the mark just before the half-hour mark after working it well down the left-hand side.
However, not long after, Gallagher whips in a ball from the left side of the area, steals the cleared ball off his fullback, who failed to check his shoulders and strikes quickly at the near post, catching the keeper out and scoring his first goal in Whites colours.
Action at both goals ensued despite there not being many chances up until the opener, as the Clarets worked it well down the left-hand side and cut it back to Alexander, who tapped in an equaliser from close range to level the scores five minutes before the break.
The Whites refused to go into the break without another chance, however, as Sommerton put in a great ball on the stretch to the back post for Sivi, but his strike was brilliantly saved off the line in the last kick of the first 45.
The Whites were the better side coming out of the interval, but Chelmsford seemed to have more possession in the opening 15 minutes of the second half.
The momentum shifted back into Brian Dutton's side right after, however, as Odokonyero had a massive chance to put in a rebounded effort in the 63rd minute after Sivi's effort, but it flew over the bar.
Less than ten minutes later, Salisbury were on the attack once more as Odokonyero whipped in a perfect cross to the danger zone, but McIntyre was just millimetres from connecting with the ball to give us the lead.
Chelmsford goalkeeper Marriott looked to make a name for himself in this tie, as Russe was denied from the edge of the area via another brilliant save.
The Whites remain unbeaten in Chelmsford for another season but feel it was two points dropped rather than one point gained.
Up next for Salisbury is the visit of winless Slough Town tomorrow evening (Tuesday, 8th September), kick off is at 7:45pm
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