The visitors took a deserved lead in the 13th minute when goalkeeper Okonkwo failed to hold onto Jordan Roberts' shot and Dan Kemp thumped in the rebound.
Things went from bad to worse for the severely under-par Welsh side five minutes later when Jamie Reid's strike from just outside the box proved too hot to handle for Okonkwo, who was having a horror start to the contest.
Kemp went close again when his fierce effort fizzed just over the bar as the half time whistle was met by a smattering of boos from the home crowd.
The Red Dragons awoke from their slumber when Oliver Rathbone netted a scrappy goal 10 minutes after the interval as Stok Cae Ras came to life. Just when another Wrexham comeback seemed on the cards, Stevenage restored their two-goal cushion with a well-worked team move which was finished off by Jake Young in the 71st minute.
Max Cleworth's towering header gave the hosts hope in the 90th minute to set up a frantic finish but Wrexham ended up losing for the first time at home since March 2024 - a 1-0 defeat to Tranmere Rovers.
Phil Parkinson's men also lost ground in the League One promotion race, with table-toppers Birmingham City and second-placed Wycombe Wanderers winning late on elsewhere on Tuesday to open the gap to third to six points.