Mata stepped off the bench to fire home a second-half equaliser after Maxi Gomez had headed Celta into an interval lead.
Gomez struck his fourth goal of the season with a thumping header from outside the penalty area following Hugo Mallo’s cross in the 33rd minute.
Getafe were quick to respond, with Jorge Molina firing an angled shot against the crossbar two minutes later and Angel Rodriguez forcing an excellent save from home goalkeeper Sergio Alvarez soon after.
Both sides continued to create chances in the second period, but it was Getafe who broke the status quo when Mata, a 66th-minute substitute for Mauro Arambarri, drove home a low shot to equalise with 12 minutes left.
Alvarez produced another crucial save to keep out Robert Ibanez’s low effort in the closing stages and Getafe goalkeeper David Soria Solis ensured a point for his side when turning away Brais Mendez’s shot.