An own goal from Sam Egerton gave United the lead six minutes before the break before Reece Kendall’s header from a corner levelled the scores at half-time.
Matt Thornhill restored his side’s lead after 66 minutes before Liam Hughes equalised again from a set piece just three minutes later in a feisty local derby.
“I’m devastated we didn’t win but is a good point for us tonight,” said Chettle.
"Getting ourselves in front just before half-time and then conceding – it’s hard to take, but it [Matlock] is a tough place to come - we played them four times last season, lost three of those times so it’s a decent result Saturday, and a good result tonight.
“They play percentage football and they are really good at set plays and we’ve had to scrap and fight tonight for that point – I think it’s deserved.”
The visitors were ahead on 39 minutes when Rev James’ low shot was deflected into his own net by Egerton.
But Basford were pegged back on the stroke of half-time when Kendall headed home from Alex Byrne’s corner.
Thornhill toed Ryan Wilson’s exquisite free-kick past Rowley to put Basford back in front on 66 minutes.
But the lead lasted just three minutes Hughes nodded home Byrne’s floated corner.
Kendall then had a volley cleared off the line by Wilson after Preston was beaten.