Universitario came from behind twice in the first half to remain level at the break and both sides seemed happy to claim a point in the second period.
The result left both clubs on 18 points with Real just ahead on goal difference, while San Jose (17 points) missed the chance to go top of the Liga del Futbol Profesional Boliviano after losing 3-1 to The Strongest on Saturday.
Real started brilliantly at home with Ivan Zerda striking in just the sixth minute but Universitario eventually hit back through Mauricio Saucedo just after the half hour.
In a frantic finish to the first half, Rosauro Rivero put Real ahead again in the 45th minute but Universitario responded immediately with Gustavo Pinedo's goal leaving the match at 2-2 at the break.
After a pulsating first half, neither team seemed willing to make a mistake after half-time, which ensured the match ended in a draw.
Sport Boys took advantage of that result and San Jose's loss to move within a point of top spot with a 3-1 win over bottom club Nacional Potosi on Sunday.
Marcos Ovejero, Leandro Ferreira and Reinaldo Parada all scored for Sport Boys as they rose to fourth position on 17 points, behind San Jose on goals scored.
The Strongest (16 points) sit fifth after second-half goals from Nelvin Soliz and Ernesto Cristaldo saw the La Paz outfit overcome San Jose, who suffered their first defeat in seven matches.
Bolivar made it two wins in a row with a 2-0 triumph over Guabira, as did Blooming, who defeated Wilstermann by the same scoreline, while Aurora and Oriente Petrolero played out a scoreless draw.
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