The home side began the day 102-2, but soon lost Adam Voges for 28 when the Australian chased a wide McLaren delivery, handing wicket-keeper Geraint Jones the first of his five second innings catches.
McLaren also accounted for Samit Patel and Matt Wood, with Robbie Joseph bowling Bilal Shafayat to leave the home side reeling at 134-6.
However, stand-in captain Read launched an entertaining counter-attack - a straight six off off-spinner James Tredwell the highlight after lunch.
But he fell 12 runs short of a deserved century when Jones clung on to a fine diving catch off McLaren.