The 34-year-old former England bowler changed the course of a rain-interrupted game as Leicestershire subsided to 42 for 5 in reply to the home side's 257.
Newport, now in his 16th season at New Road, enjoyed a spell of 4 for 20 in 12.5 overs, spanning two intervals and three hold-ups for rain. Iain Sutcliffe was lbw to the first ball after lunch, Aftab Habib and Vince Wells edged successive deliveries, and Neil Johnson also fell leg- before.
Leicestershire had started the day by taking Worcestershire's last four wickets for 58. Alan Mullally finished with 4 for 86 and Gavin Haynes was unbeaten on 47 for Worcestershire.
Monte Lynch played through rain and bad light for a sparkling half-century as Glou- cestershire closed in on Hampshire's 316 at Bristol.
Lynch had put on 71 with Rob Cunliffe (43no) when Gloucestershire accepted the offer of the light at 143 for 2.
Earlier a stand of 77 for the seventh wicket between Shaun Udal and Bill Kendall boosted Hampshire from their overnight total of 221 for 6. Mike Smith's slow left arm took 4 for 61 for Gloucestershire.
David Lawrence, playing his first game for Gloucestershire for five years after a twice broken kneecap, had to leave the field after three overs of declining speed. He headed for the treatment room and was not seen again. The official reason was "a minor strain to the right calf".Reuse content