Lisa Topping opened the scoring for the visitors just ahead of half-time with an impressive long-range effort before United hit back after the interval.
In the 65th minute, Whites winger Paige Williams squared the ball to Smith on the edge of the area, and the midfielder turned smartly past Chorley defender Megan Searson before firing into the roof of the net.
Leeds had the chance to take the lead minutes later when the referee pointed to the spot after Rebekah Bass was felled inside the box by Rachel Hindle, but Sarah Danby's penalty was saved.
The result sees Dan O'Hearne's side remain in third place in the Division One North table, with the gap to second-placed Newcastle closed to 11 points.
Sunday's contest marked the Whites' return to league action for the first time since they played Durham Cestria on October 10, with FAWNL Plate and County Cup ties filling the fixture schedule in the meantime.
With the extended period away from Division One North leaving them two games behind the teams above and below them in the table, Smith claims the disruption makes competing difficult.
"It's so frustrating," Smith said.
"You try and get some momentum in the league - we were doing well and winning games - then obviously got to winter time and loads of cups that we played in.
"That disrupted us, and then games off because of the weather.
"I think Dan said it was 112 days since we last played a league game, which is ridiculous really."
On Wednesday, United will travel to ninth-placed Barnsley in the hopes of further shortening the gap to second place.
Smith, who departed Barnsley to join the Whites last summer, insists that Sunday's draw has left Leeds hungry for the midweek clash.
"I can’t wait for Wednesday, bit of a derby day, so bittersweet I think," Smith told LUTV.
"We’re all up for it, especially going in off the back of that [Chorley tie].
"We know we can perform."
Leeds will take on Barnsley at Wombwell Recreation Ground on Wednesday, with kick off at 7.45pm. Tickets cost £3 for adults and £1 for Under-16s.