The 25-year-old playmaker replaced full-back Alvaro Arbeloa in the 81st minute of the Group I World Cup qualifier in Tbilisi and within five minutes had conjured the crucial assist for Roberto Soldado's winner in a laboured 1-0 success.
It was the latest in a series of decisive interventions for Spain by the former Arsenal captain, including the pass that set up Andres Iniesta to score the winning goal in the 2010 World Cup final and the cross for David Silva to net the opener against Italy in the Euro 2012 final.
Coach Vicente del Bosque praised Fabregas for his "movement and intelligence" after the Georgia game, Spain's opener in a group which also includes France, Belarus and Finland.
Patience had been the key to victory against a side using the kind of ultra-defensive tactics Spain have become used to in recent years, he added.
"We had various options to try to break through the opposition defence... and in the end the gap opened up," Del Bosque said.
"It wasn't about getting nervous but having patience and playing in the most orthodox way possible because otherwise we would have exposed ourselves to the counterattack, with the obvious danger that carries with it."
Fabregas had an impressive start at Barca last season after returning to his boyhood club but his form tailed off and former coach Pep Guardiola overlooked him for some key matches in the Champions League and La Liga.
Under Guardiola's replacement, Tito Vilanova, he has yet to make much of an impression this term and was an unused substitute in last month's Spanish Super Cup defeat to arch rivals Real Madrid.
He fluffed two clear chances in Barca's 1-0 La Liga win at home to Valencia this month but has a chance to redeem himself on Saturday when the leaders seek a fourth win in four games at Madrid-based side Getafe.
- Andres Iniesta