The 20-year-old striker (pictured playing for Celtic) struck after seven minutes to cancel out Kaimar Saag's early opener, and Don Givens's side could easily have returned with all three points after outplaying the current leaders of Group 2.
Ireland went into the game desperate for points following their 3-0 defeat by Turkey in Cork back in March, while Estonia had beaten Switzerland and Georgia in their opening two matches.
It looked like going horribly wrong after just four minutes, however, as Saag beat Burton Albion keeper Shane Readman to get the hosts off to the ideal start.
Sheridan's goal three minutes later was the beginning of a concerted Irish effort to surge forward in search of a winner, but the remaining 83 minutes were goalless.
Ireland are left in fifth place in the group, six points behind Estonia and five behind Turkey and Switzerland, all of whom have played a game more.