Gillingham were denied a fourth straight win after conceding a stoppage-time penalty.
The Gills had been a goal down in a tricky League 1 match before John Marquis levelled and Luke Norris struck with two minutes left.
But Gillingham’s celebrations were hushed when the hosts claimed a share of the spoils with a penalty at the death.
Yeovil started the afternoon bottom of League 1 but made four new signings in the lead up to Gillingham’s visit.
Defenders Byron Webster (Millwall) and Stephen Kingsley (Swansea) joined the club along with midfield pair John Sheehan (Swansea) and Craig Eastmond.
The Gills were in search of a fourth straight win in the league to give their play-off hopes more credibility. Justin Edinburgh’s side were four points adrift of the top six ahead of their trip to Huish Park.
Edinburgh named an unchanged starting XI for the match. Josh Pritchard was the only new face in the squad, coming in as substitute and replacing Antonio German.
Saturday’s game took a while to kick into life and it was from the game’s first shot at goal that Yeovil took the lead. Samuel Foley’s free-kick was helped on by Webster and Chigozie Ugwu crashed home the loose ball.
Gills’ claims for handball and/or off-side fell on deaf ears.
Yeovil almost got a second moments later when Danny Galbraith lost the ball and the hosts broke. It took a save from Stuart Nelson and a block from Gavin Hoyte to deny James Hayter.
Cody McDonald headed a chance wide for the Gills, following a good spell of possession football from the visitors, but Yeovil ended the half on top. Only desperate defending denied them another before the break when Joshua Sheehan’s free-kick into the area caused panic at the back for Gills.
A change at the break saw Jermaine McGlashan replace Galbraith and a change in formation saw the Gills switch to 3-4-1-2.
The Gills hit back just five minutes after the restart when McDonald’s low free-kick was spilt by keeper Artur Krysiak and Marquis pounced from close range.
McDonald went over in the box just before the hour mark under a heavy challenge but referee Simon Hooper, not for the first time, waved away Gillingham’s appeals.
Edinburgh’s side were much improved after the break, limiting Yeovil to half-chances. Liam Shephard lashed a chance wide from distance and Nelson had to be alert to hold onto Sheehan’s drive.
The Gills keeper was at full stretch to deny Samuel Foley as he also tried his luck from long range.
With two minutes left Gills sub Norris made room for himself on the edge of the box and drilled in a low shot, into the bottom corner, to put the visitors ahead.
Yeovil weren’t finished, however, and when Gavin Hoyte fouled Joel Grant in the box, the referee pointed to the spot and Morgan smashed home the penalty to level.
Yeovil: Krysiak, Smith, Berrett (Morgan 77mins), Hayter (Grant 62mins), Foley, Ugwu, Arthurworrey, Webster, Sheehan, Shephard, Kingsley. Subs: Stewart, Moore, Twumasi, Davis, Eastmond, Morgan.
Gillingham: Nelson, Hoyte, Garmston, Egan, Ehmer, Loft, Hessenthaler, Galbraith (McGlashan 46mins), Dack (Pritchard 89mins), Marquis, McDonald (Norris 83mins). Subs: Martin, Legge, G Morris, Pritchard, Dickenson.
Attendance: 4,293 (458 away)