Paul Mullin opened his tally for the 2022/23 season, but a second-half wonder-strike by Malachi Linton ensured the points were shared at Huish Park.
In extreme heat – which meant each half was punctuated by a drinks break midway through – Mullin coolly slotted in an early opener.
Linton levelled from distance just after the break, however, and neither side could find a winner to leave Wrexham with a win and a draw from the opening two games.
Phil Parkinson made three changes from last weekend’s opening-day win against Eastleigh, with all three players to have featured off the bench handed starts this time out.
Jordan Davies replaced injured Tom O’Connor, while Jacob Mendy and match-winner Elliot Lee were in for Callum McFadzean and James Jones.
Mullin raced onto a long clearance and fired beyond Yeovil keeper Smith just six minutes in to give the Red Dragons the lead.
Chances were at a premium, however, and Yeovil defended well to block efforts from both Lee and Ollie Palmer before the break.
Mark Howard had already saved well from Linton as Yeovil made the better start to the second-half, before the spectacular equaliser on 49 minutes.
Linton’s half-volley arced into the back of the net to level the scores, and for a short period afterwards put the visitors in the ascendancy.
Neither side could add to the score, however – Palmer going closest for Wrexham when he closed down Smith’s clearance but could not escape the keeper’s attentions to prod the ball in.
A stop-start game lacked rhythm, and Wrexham now travel to Chesterfield for Tuesday night’s clash with four points to their name from the opening two Saturdays of the 2022/23 campaign.
Wrexham (3-4-1-2): Howard, Hayden, Tozer, Cleworth, Forde, Young, J.Davies, Mendy (Hosannah 62), Lee (J.Jones 68), Mullin, Palmer
Subs not used: Watson, Tunnicliffe, Dalby
Yeovil Town: Smith, Williams, Hunt, Wakefield, Staunton Reckord, Worthington, Perry, Pearson (D’Ath 68), Linton (Johnson 87), Fisher (Toure 71).
Subs not used: Pond, Buse