Coach Peter Woods' team were unable to force a victory they desperately needed in a final period that they dominated.
Britain still top the table by one point, but must now hope Denmark pull off a shock victory in Kloten on Saturday. Even if the Swiss are held to a draw they will claim the group on superior goal difference.
Britain could not have had a worse start as Manuele Celio duly made by scoring on the powerplay, though the lead lasted less than a minute as Basingstoke's Richard Little forced home an equaliser from close range.
Switzerland's superior stickwork eventually got them a second goal, though again it came with a British player - Mike Bishop - serving a two-minute penalty for tripping.
Dino Kessler looked set to pass, but suddenly unleashed a long-range effort that screamed past unsighted netminder Bill Morrison into the top corner.
But Cranston made amends for his earlier penalty by grabbing an equaliser just 39 seconds before the end of the first break.
And from Britain's first serious attack, more than five minutes after the break Cardiff's Canadian-born forward Doug McEwen ended a sudden flurry of activity around the visitors' goal by scoring with a low shot.
The Swiss deservedly levelled to leave the tie finely balanced going into the last period, though there was a huge slice of fortune about their equaliser.
Vjeran Ivankovic's tame effort from virtually parallel to Morrison's goal somehow found the narrowest of gaps to trickle in off the netminder's skate.Reuse content