The decline was due to a fall in food prices and smaller increases in fuel costs.
Meanwhile, the country's industrial output in December rose 2.4 percent from a year earlier, slightly higher than forecast, government data showed on Tuesday.
The RBI also reduced repo rate by 25 bps, after retail inflation hit an 18-month low in December to rise 2.19 percent, led by softening crude oil prices and cheaper food items. It softened to 5.4 percent in January, according to economists at Yes Bank Ltd. and Axis Bank Ltd. Pranjul Bhandari, chief India economist at HSBC Holdings Plc, sees it slowing to as low as 4 percent this year. B Prasanna, head, Global Markets Group, ICICI Bank said, "The CPI number surprised positively and core inflation also moved lower".
"This reinforces expectations of a rate cut in April", he added.
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Mining sector output contracted by 1 per cent in December as against 1.2 per cent growth in December 2017, the data showed. Consumer-price growth reached 2.05 percent in January, well below the Reserve Bank of India's medium term target of 4 percent.
For now, headline inflation eased further as food prices extended their fall, albeit at a slower pace.
Prime Minister Narendra Modi, who faces tough general elections by May, has announced an annual transfer of 750 billion rupees ($11 billion) to millions of farmers, and tax benefits for the middle class, which many economists say could spur both consumer spending and inflation.
Shaktikanta Das, the RBI's new governor, voted for a cut despite only weeks earlier acknowledging the challenges posed by the divergent paths taken by core and food inflation. The figures show rural incomes remain under pressure while consumers benefit from easing inflation.
A Reuters poll of 30 economists had predicted CPI to have accelerated to 2.48 per cent in January.
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