The hosts had claimed more points per game on home soil than any other side in the division ahead of kick-off.
But, as they did in their 1-0 victory against Oxford United three days earlier, Wrexham started on the front foot as Sol Brynn denied Ryan Longman in the sixth minute.
After going short from the resulting corner, George Thomason fed Windass whose shot struck Dael Fry before sailing beyond Brynn.
The visitors were dealt a blow midway through the first half as Lewis Brunt – starting in place of the suspended Callum Doyle – was forced off through injury, with Dan Scarr coming on in his place.
But the Welsh side still carried the greater threat as summer signing Windass had another effort blocked as Boro went into the break behind having failed to register a shot on target.
Rob Edwards responded by making four substitutions ahead of the second half – with Luke Ayling, Sam Silvera, Tommy Conway and Alan Browne replacing Matt Targett, Delano Burgzorg, Sverre Nypan and Morgan Whittaker.
Middlesbrough grew in confidence as Wrexham goalkeeper Okonkwo made a routine save to deny Tommy Conway on the hour mark.
Sensing the home side’s improvement, Phil Parkinson sent on Nathan Broadhead, Liberato Cacace and Lewis O’Brien on 65 minutes – with goal scorer Windass, Ryan Longman and Thomason making way.
The visitors should have doubled their lead shortly after that trio of substitutions as O’Brien crossed for Kieffer Moore who could only head against the crossbar from close range.
And they were left to rue that miss 10 minutes from time as Hackney rose to meet Brittain’s cross to head into the net at the back post for his second goal of the campaign.
Just three minutes after levelling proceedings, Hackney was denied from a free-kick by Okonkwo as the home side pushed for a winner.
But the contest ended level as Boro extended their unbeaten record at home this term while Wrexham missed out on claiming back-to-back league wins for the first time this season.
