Swindon seemed to suffer a Paolo Di Canio hangover in a lacklustre first-half display, coming after the Italian's resignation last week.
Town's temporary management duo of established first-team players Tommy Miller and Darren Ward saw Preston take the lead in the 51st minute through Will Hayhurst.
The hosts had to wait until the 75th minute to level when Adam Rooney, who had only been on the pitch a matter of seconds, latched on to a poor back pass from David Buchanan to beat Rudd.
"I am pleased with our performance. We kept our shape and organisation against a team at the top of the league," said Grayson after the 1-1 draw.
"We limited Swindon to just a few clear opportunities and our only mistake led to their goal.
"This display will stand us in good stead and the aim now is to win as many games as possible to serve as a platform for next season.
"I have got to get to know the players and I will not be trying to do too much, too soon."