Both the teams had already qualified for the semi-finals after winning their ties against Kerala and Delhi, the other two teams in Group A.
The first goal came just 15 minutes into the match when Ayan Choudhury's shot found the net for West Bengal.
The defending champion maintained their one goal lead late into the match. The equalizer came for Asom in the 82th minute when Sunil Basumatry scored for the host team.
In the other Group A match of the day, Kerala beat Delhi 2-1.
with both teams already out of the race, the result had no bearing on the semi-final line up.
Both the goals for Kerala were scored by V V Farhat in the 21st and 43rd minutes. Kulbhusan Manderwal was the lone scorer for Delhi in the 39th minute.
With today's matches, the league stage is over.
In the first semi-final on May 24, Asom will take on Punjab, while on May 25, West Bengal will play Goa.
The final is slated for May 27.