In the process Smith denied Swindon a great chance to keep up the pressure on League Two leaders Walsall.
Smith took over from Alun Armstrong in the 62nd minute and nine minutes later had plenty of time to convert a pass from Gregg Blundell, which had split the Swindon defence.
Smith had no trouble in beating his namesake, Swindon goalkeeper Phil Smith, with a low left-foot shot.
Swindon had only themselves to blame for not making the most of a host of inviting chances.
All they had to show for their first-half domination and complete control of the match was a goal after 10 minutes by full-back Andy Nicholas.
Jamie Vincent took a free-kick deep into the Darlington penalty area and, as the defence hesitated, Nicholas ran through to head into the empty net from six yards for his first of the season.
There should have been many more Swindon goals and they went close several times, none closer than in the 12th minute in an incident involving the lively Christian Roberts.
Roberts beat goalkeeper Lee Jones with a 25-yard volley but the ball rebounded from the bar and Roberts could only head the rebound wide.
Lee Peacock headed just wide from a centre by Jack Smith, and Aaron Brown sent a left-foot shot flashing across the face of the goal.
Roberts should have done better in the 38th minute when a centre from Brown found him unmarked at the near post, but the Swindon striker carelessly sent a left-foot shot wide, when it looked easier to score.
Darlington offered nothing in the way of attacking movements or chances in the first half and Swindon's domination continued into the second.
Michael Cummins carelessly mis-hit wide from 15 yards in the 66th minute and a great save from Lee Jones, rushing out to push away a header from Peacock, saved Darlington from conceding again.
But the match turned on its head in the last 20 minutes after Smith had scored Darlington's equaliser. First Smith headed narrowly wide and another substitute, Tommy Wright, hit the underside of the Swindon bar with a close-range shot.