The Guardian Lonergan poll of 958 voters taken on Wednesday night gave Dr Glasson a 52-48 lead in two-party terms.
While the poll had a four point margin of error, it is likely to raise concerns for Labor with 16 days to go before election day.
The prime minister's primary vote was 38 per cent - down six points on his 2010 election result - while Dr Glasson had 47 per cent of the primary vote.
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