The Markit Eurozone Services Purchasing Managers Index (PMI), which surveys more than 2,000 businesses ranging from banks to hotels, rose in November to 55.4 from 53.3 in October and beating an earlier flash estimate of 55.2.
This marks the 15th month the index has kept above the 50 mark that divides growth from contraction, largely thanks to strong private sector recoveries in the biggest of the 16 euro zone economies, Germany and France.
However, surveys released earlier on Friday showed the Spanish service sector in decline and Ireland's in stagnation – a divergence from the prosperous euro zone core which survey compiler Markit warned could worsen in coming months.
"Germany's recovery goes from strength to strength as service providers and consumers feel the benefit from export-led growth," said Chris Williamson, chief economist at Markit.
"But austerity measures and economic uncertainty are hitting consumer confidence in the debt-laden countries."
Underlining the divergence, Williamson noted that business expectations in Germany hit their second highest in almost seven years while Irish confidence in the future saw the biggest monthly deterioration since the collapse of Lehman Brothers.
For the eurozone as a whole, order books at services companies grew at the strongest rate since August, with the new business sub-index rising to 53.2 from the flash estimate of 52.9 and October's 52.1.
The services jobs index hit its highest level since February 2008 and again thanks to a strong German recovery, with business expectations also improving.
The composite PMI survey, which combines data from the services index with Wednesday's manufacturing PMI, also rose strongly on the back of Franco-German strength.
The headline composite index reached 55.5 in November from 53.8 in October, revised up marginally from the flash reading of 55.4.
"The final Eurozone PMIs highlight the dilemma facing policymakers at the ECB due to growing variations in economic recoveries within the region," Williamson said.
"Spain is showing further signs of double-dip recession, with output contracting for the third successive month and Ireland barely managing to stagnate."
The composite PMI did show some promising news on jobs growth, however. At 53.1, the jobs sub-index hit its highest level since February 2008, rising from 51.1 in October.
Unemployment in the euro zone inched up to 10.1 per cent in October from 10.0 per cent in September, its highest level since 1998, according to official statistics released on Tuesday.