Following an uneventful start to proceedings, Wrexham’s control grew as the first half wore on – with Radek Vitek keeping out a tame Callum Doyle header.
And the Red Dragons went ahead on 34 minutes as Doyle’s cross struck George Tanner before falling into the path of Rathbone who instinctively lashed into the net from 10 yards out.
Following his side’s lacklustre showing in the opening 45, Gerhard Struber sent on Armstrong, Delano Burgzorg and Knight at the break.
Tomi Horvat forced Arthur Okonkwo into a smart save just 15 seconds after the restart as the hosts swiftly got on the front foot.
And Armstrong rifled beyond Okonkwo from a narrow angle a minute later to end his seven-game run without a goal.
Nathan Broadhead and Armstrong both had efforts to put their side ahead as the contest produced more goalmouth action.
Williams replaced the injured Adam Randell as Phil Parkinson sent on top scorer Kieffer Moore, Josh Windass and George Dobson with 20 minutes remaining.
And the Welsh side regained the lead in the 76th minute as Issa Kabore’s cross was turned into his own net by Williams.
Dobson spurned a golden opportunity to seal victory nine minutes from time as he dragged a shot well wide following slick build-up play between fellow substitutes Windass and Moore.
They were made to pay for that miss as Bird produced a moment of quality to make it 2-2.
Dobson thought he had one final chance to earn his side all three points, but he could only turn Windass’ cross wide in the third minute of added time, although the offside flag had been raised as the contest ended level – with both sides missing the chance to move into the top six.
