Medo Kamara put Bolton into the lead after 65 minutes by placing a free-kick into the corner of the net.
But Town managed to score just eight minutes later through McGoldrick's left-footed strike to leave the Trotters still fighting for their second win of the season.
Bolton made two changes from their last match. Andy Lonergan replaced the injured Adam Bogdan in goal and David Ngog came in to the starting line-up after Liam Feeney was recalled by his parent club Millwall.
Ipswich were able to name both Dean Gerken and Daryl Murphy from the start, despite having injury fears for the pair.
Bolton had the first chance in the opening exchanges after Jermaine Beckford's acrobatic effort went just inches over the bar.
Town then fired back, though, with the best chance of the half. A great move between Luke Hyam, McGoldrick and Ryan Tunnicliffe looked to have given the Tractor Boys the opener, with McGoldrick squaring the ball to Ryan Tunnicliffe, who just had the keeper to beat.
But Lonergan produced a brilliant one-on-one save to deny the on-loan Manchester United midfielder.
Beckford then had another chance when Ngog played a ball back on the inside to the Jamaica international, who turned his shot wide which made sure it stayed level at the break.
The Trotters then started the second half the brighter with Chung-Yong Lee looking threatening.
The South Korea international's rifled shot from outside the box forcing Gerken into turning the ball over for a corner.
However, the visitors still looked strong on the counter as Daryl Murphy cut back inside in the box and had a go, with his shot deflecting agonisingly close to the post.
Beckford's pace then troubled the Ipswich back four, and, just as he looked to be through on goal, Christophe Berra committed a cynical foul on the edge of the area.
After a booking was brandished at the defender, Kamara stepped up and slotted the free-kick through the grips of Gerken's left glove to give the home side the lead.
It was not to last long though, as Town equalised shortly after.
Cole Skuse's effort was blocked but the ball then fell to McGoldrick, who made no mistake when rattling the ball past Lonergan from outside the box.
Substitute Frank Nouble then almost played in McGoldrick once more but the former Nottingham Forest striker could not get a decent shot away, which allowed Bolton to extend their unbeaten run to five games.