Housing, recreation and culture, alcohol and tobacco, and communication had the biggest price increases over the most recent quarter, according to the Australian Bureau of Statistics.
Underlying or trimmed-mean inflation is the RBA's preferred measure because it ignores volatile items such as power prices.
The previous reading in June was 2.7 per cent.
Headline inflation, which covers a broader swathe of the economy, jumped to 3.2 per cent over the year to September, largely because of changes to government energy bill rebates in some states.
The Reserve Bank's target band for inflation is between two and three per cent.
Analysts were widely expecting inflation to rise, but the figures were stronger than anticipated.
The quarterly data is the last major piece of the puzzle before the Reserve Bank announces its next interest rate decision on Tuesday.
The official cash rate is at 3.6 per cent, with higher-than expected unemployment figures for September boosting expectations of a rate cut.
But Ms Bullock said in a speech on Monday she was relatively unfazed by the jump in unemployment, with signs the jobs market was still tight.
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