Maher shared an opening stand of 78 with former captain Jon Lewis until Lewis fell lbw to spinner Dalrymple when attempting to sweep.
With wickets falling around him, Maher was patient but attacking when possible. His 106 came from 207 balls and when he was out he had scored more than half of Durham's total of 208-6.
With Durham looking in some trouble, Phil Mustard and Ottis Gibson put on a stand of 88 with Gibson scoring 38 and Mustard finishing on 78, to add to his 130 in the first championship match of the season.
Graham Onions added some late runs as Durham finished the first day on 340-9. Mick Lewis added eight runs on Thursday morning before falling lbw to Louw to see Durham all out for 348, just two runs short of a fourth batting point but well ahead of what could have been expected at tea on the previous day.
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