The group saw organic service revenue - a closely-watched measure of sales - rise 1.4% to £9.2bn in the three months to the end of December last year, beating the 1.2% rise in the previous quarter.
It was buoyed by "strong" service revenue growth in its India and South African businesses, which grew 2.3% and 7.2% respectively in the third quarter.
The Newbury-based company also saw a brightening picture across Europe, with service revenues continuing to recover, down 0.6% in the three months to the end of December last year, compared to a 1% drop in the previous quarter.
The group also confirmed that it was on course to hit full-year earnings before interest, tax, depreciation and amortisation of between £11.7bn and £12bn.
Shares in the FTSE 100 company were up 2% in early trading as investors digested the financial update, which came just days after it confirmed talks were under way with cable firm Liberty Global over a joint venture in the Netherlands.
Vodafone - which had decided to abandon talks with Liberty Global six months earlier over a possible asset swap - said the discussions were ongoing and stressed they "do not extend beyond the creation of a joint venture in the Netherlands."
Vittorio Colao, Vodafone group chief executive, hailed the boost in service revenues over the third quarter, stating the business had taken "another step forward in the last three months".
He added: "We continue to face regulatory and competitive challenges in many markets, but we are confident that the business is well positioned for the growth opportunities ahead."
In Germany, service revenue fell 0.4% in the third quarter, compared to a 1.8% drop in the second quarter, while in Italy service revenue was down 0.3% over the period, compared to a 2% fall in the second quarter before.
But in the UK, service revenue dipped 0.7% in the three months to December 2015, against a 0.5% decline in the second quarter, as a boost to its fixed service business was offset by a fall in mobile revenues.
The company added 506,000 new European mobile contract customers to its books over the period alongside 311,000 broadband customers.
Charlie Huggins, analyst at Hargreaves Lansdown, said: "Vodafone is broadening services out beyond mobile and into broadband, cable TV and fixed lines, moving toward the Holy Grail of quad-play services, one market at a time."