Goals from Jonathas (61st, penalty) and a last-minute equaliser from FC Goa striker Romario (90+5) meant that neither team would take away three points.
The result prevents Odisha from rising to fifth place in the standings, level on points with Bengaluru FC and Kerala Blasters FC. As for FC Goa, the winless run extends to five games.
Plenty of end-to-end stuff was observed in the starting few minutes by both teams. The Gaurs had a bigger share of the possession but struggled to translate it into scoring opportunities.
Airan Cabrera got space behind the Odisha defence at the first quarter of the hour but ended up shooting above the crossbar.
On the other end, Liridon Krasniqi missed a great opportunity to score owing to brave goalkeeping from Naveen Kumar.
Arshdeep Singh also had to pull off a strong save from Edu Bedia right after the drinks break. Princeton Rebello thought he had scored at the 40th-minute mark until Thoiba Singh made a goal-saving block inside the box.
Both teams lacked inspiration in the attack, leading to no goals at the half time break.
After the restart, Cabrera demanded a penalty for a potential handball but to no avail. The striker got his shot past the goalkeeper but saw it blocked by the defender, seemingly with the hand.
However, right at the hour mark, the Kalinga Warriors were awarded a penalty after Javier Hernandez was tripped by Alberto Noguera inside the box.
Jonathas stepped up and sent his spot-kick into the top left corner for the breakthrough goal.
A few minutes later, Jerry Mawihmingthanga came close to extending Odisha’s lead but his chip hit the crossbar.
Derrick Pereira made several changes heading into the last stage of the match, pushing for the equaliser.
Four minutes were added for stoppages which saw more pressure from the Gaurs, looking for that elusive equaliser. It finally came through Romario who scored through a header in the final minute of the added time, thus sharing the points between both sides.