Depor, the only team apart from the top two in with a realistic chance of taking the title, went ahead just before halftime with a cracking Albert Luque free kick.
Javier Irureta's side had plenty of chances to add to their lead but Javi Guerrero provided Racing with a spectacular equaliser in the 77th minute.
A draw left Deportivo in third place on 37 points at the halfway stage in the season, six points behind Valencia and five behind Real Madrid.
Valencia dislodged Real at the top of the table, and took the honorary title of winter champions into the bargain, when they beat Albacete 1-0 on Saturday and Real went down 1-0 at Real Sociedad.
Atletico Madrid climbed up to fourth place on Sunday with 31 points with a 3-0 win at home to Athletic Bilbao, featuring two goals from Fernando Torres.
Villarreal are fifth, a point further back, after a 3-1 win at home to Valladolid, while Barcelona moved up to seventh on 27 points with a morale-boosting 3-0 win over Real Zaragoza at the Nou Camp.
Deportivo, the 2000 league champions, were under pressure for much of the first half against ambitious Racing, who hit the frame of the goal twice before the home side had really settled.
Ayoze had the first chance, surprising Jose Molina with a cross-shot that struck the far post after 20 minutes.
Ten minutes later, Guerrero hit the bar with a neat chip and Pablo Casar caused the Depor defence more nervous moments with his header around the half-hour mark.
Depor responded by taking the lead with Luque's eye-catching free-kick just before the break and they dominated in the second half.
Chances came and went, however, and Racing clinched a point when Guerrero took a long pass from Anderson Silva and beat Molina with a first-time lob.
