In a frantic affair in Cheshire, Artur Krysiak made two smart stops in the first half whilst Ryan Seager went close to netting at the other end on two occasions.
After the break both sides searched for an elusive winner and Sam Surridge had the ball in the net but for an offside flag, but it remained goalless as Town moved four games unbeaten in all competitions.
Darren Way made three changes from the eleven who recorded back-to-back league victories over Grimsby and Cambridge United.
Man of the Match in Town’s Checkatrade Trophy quarter-final win in midweek, Corey Whelan made his first league start for the club, coming in for Ryan Dickson.
In a midfield reshuffle, Rhys Browne replaced Alefe Santos in a switch which saw Jake Gray revert to a more central position to accommodate the winger.
Completing a change in each department, Surridge dropped to the bench as Seager made the starting eleven for the first time since arriving in January against his former employers.
On a boggy Gresty Road pitch, it was something of a midfield tussle in the opening half an hour with chances at a premium.
Unable to penetrate two resolute defensive units the Glovers had to make do with half-chances, as Seager blazed over from an unlikely angle before Lewis Wing struck a well-hit effort just wide from 25 yards.
Degenerating into a match played largely in the middle of the park, it took until 27 minutes for either ‘keeper to be called into action.
Working possession cleverly down the left, Alexandra worked the ball into Callum Ainley on the left-hand side of the box only for his stabbed strike from the angle to be kept out by Krysiak.
Becoming an important figure for the visitors the Polish stopper was in action again two minutes later, getting everything behind a fiercely hit Zoumana Bakayogo shot from inside the box.
Responding at the other end, Seager saw a strike fly inches wide from the edge of the box, before the two defences prevailed once again to keep it goalless at the halfway stage.
Looking for a fourth straight win, Yeovil were dealt two blows in quick succession in Cheshire.
Picking up an injury in the first-half, Nathan Smith was replaced by Dickson at half-time before the ever-present Krysiak had to be withdrawn.
Brilliantly tipping Harry Pickering’s free-kick onto the bar, the Pole picked up a knee injury in the process and with a little under 40 minutes remaining was replaced by Jonny Maddison for a first appearance of the season.
Opening up as an encounter to create more chances, Shaun Miller zipped an effort over the bar whilst Omar Sowunmi couldn’t direct Tom James’ shot on target.
Ticking past the hour mark, Francois Zoko sold three Crewe players with a dummy before drilling a shot across the face of goal whilst at the other end Ainley drew a smart save from Maddison.
Defending manfully, the Glovers searched for a winner in the final 20 minutes as Wing blazed a duo of long-range efforts over the bar, whilst substitute Surridge was denied a dramatic winner in the 89th minute by the linesman’s flag following a good passing move.
Unable to find a winner, both sides had to settle for a share of the spoils as the Glovers continued their good run of recent form.
Crewe Alexandra: Garratt; Sterry, Ng, Nolan, Bakayogo; Ainley, Green, Pickering, Kirk (McKirdy 64′); Miller, Bowery.
Subs not used: Richards, Walker, Raynes, Lowery, Reilly, Barlaser.
Yeovil Town: Krysiak (Maddison 51′); Whelan, Sowunmi, N. Smith (Dickson 46′), James; Green, Wing, Gray, Browne; Zoko, Seager (Surridge 68′).
Bookings: Whelan 21′, Dickson 90′
Subs not used: Bird, Gobern, Santos, Fisher.