In an open and entertaining game it was Boro who dealt the first blow just after the hour-mark when Marvin Emnes' flicked header gave the visitors the lead.
Lukas Jutkiewicz then hit a post but Brighton got the equaliser their play warranted when Calderon met Kazenga LuaLua's corner with a thumping header.
It was Middlesbrough's fourth successive 1-1 draw and, although they have now failed to win in six, they hold a two-point cushion over Cardiff in the final play-off spot.
The Bluebird's draw with Millwall ensured the game kicked off with both sides occupying the final two npower Championship play-off places.
Brighton were slow to get out of the blocks at Nottingham Forest last week and both they and their opponents were tentative in the early exchanges.
Left-back Joe Mattock displayed some urgency when he ventured forward, latching onto Sam Vokes' diagonal pass before hitting a venomous strike which was parried away by Jason Steele.
At the other end, Barry Robson's powerful free-kick flew narrowly over Peter Brezovan's crossbar.
Brighton's opening goal at Forest came via a Vicente free-kick and the Spaniard nearly replicated that feat when his set piece took a huge deflection off the wall before dropping just wide.
Seagulls boss Gus Poyet had welcomed Will Buckley back into the fold and he conjured up another great chance moments later, fizzing a corner into the near post which Adam El-Abd touched against a post.
Middlesbrough, clearly recognising the need to snap their winless streak at this stage of the season, poured forward with Jutkiewicz drilling low straight into Brezovan's arms.
His strike partner Emnes had the first real chance in the second period, shifting the ball onto his left foot before driving just wide.
The lively Vicente tried to better Emnes with a left-foot try of his own but Steele got down well to push the ball clear.
But Middlesbrough's attacking endeavour was rewarded when the visitors snatched the opening goal in the 61st minute.
Robson's inswinging corner was flicked on by Emnes at the near post with Brezovan, who had been impressive up until that point, caught out of position as the ball flew in.
Boro continued to win the midfield battle and they nearly doubled their advantage when Jutkiewicz had a shot come back off a post.
But it was Brighton who got a leveller 17 minutes from time as Calderon nodded in Lua Lua's corner at the back post.
Vicente's set pieces continued to create havoc in the Boro penalty box and Vokes met another free-kick with a header which Steele had to parry away.
Both sides surged forward in search of a winner but neither side could find a way past the busy goalkeepers.