Charlie Austin's 85th minute equaliser denied Town all three points at The County Ground as the former Premier League striker's header cancelled out Anthony O'Connor's opener.
Simon Weaver made four changes from Tuesday night as Warren Burrell captained the side from right back, Stephen Dooley returned to the midfield George Thomson took his place back on the right and Jack Muldoon returned to lead the line.
The hosts also made four changes to their starting XI with Harry McKirdy leading the line and Charlie Austin taking a spot on the bench.
Harrogate Town started brightly and worked an early opening for Matty Daly, but he couldn't get his finish right after direct attacking play from Abraham Odoh down the left.
Aaron Drinan was looking the most lively for the hosts as he got in front of Liam Gibson and headed wide after 15 minutes, before firing wide nine minutes later in what would be the closest the hosts would come in a first half with few goalscoring opportunities.
Town's best opportunity of the half came as Odoh and Daly combined again, this time it was Odoh who was close to finding the finishing touch.
Town had some defending to do at the end of the half with Matty Foulds and Jack Muldoon both making telling contributions, but we're forced into a change just before half time as Joe Mattock replaced the injured Liam Gibson.
Swindon made a double change at the break as Paul Glatzel and Rushain Hepburn-Murphy were introduced, but it was Town that would get their noses ahead seven minutes after the restart.
O'Connor threw himself at George Thomson's free kick delivery to guide his header past Jack Bycroft and mark his 500th career appearance with a goal.
The Irish centre half was involved at the other end five minutes later to keep the hosts out who had responded well to going behind, scrambling Glatzel's effort off the line.
There were penalty appeals, near misses and some resolute defending in the latter stages of the game, but Swindon were becoming increasingly frustrated at their inability to break Harrogate down.
The pressure kept mounting though and eventually paid off on 85 minutes when substitute Austin produced a delicate header that looped into the back of the net. The former Premier League forward denying Town a first win at The County Ground.