John-Lewis' 24th minute toe-poke extended Lincoln's unbeaten run to seven matches and left Bournemouth stuck on minus four points.
Bournemouth were unlucky not take the lead after only three minutes when Darren Anderton's left-wing corner caused havoc in the Lincoln defence.
The ball broke kindly for Lee Bradbury, whose fierce half-volley from six yards was stopped on the line by Imps goalkeeper Rob Burch.
Bradbury's anguish intensified 20 minutes later when John-Lewis put Lincoln in front with his first goal since August.
Full-back Paul Green came bursting down the right wing and picked out John-Lewis with a teasing low cross.
He prodded the ball towards the bottom left corner and Bournemouth goalkeeper Shwan Jalal could only palm the shot into his own net via the post.
Anderton carved out a good chance for Danny Hollands with a cleverly worked 32nd minute corner, but the former Chelsea reserve hammered his shot over the crossbar from 20 yards.
Former non-league striker Jeff Goulding had Bournemouth's first attempt of the second half when he put a mis-hit shot into the arms of Burch from 18 yards.
Stefan Oakes threatened to extend Lincoln's lead on the hour when he fizzed a 25-yard free-kick inches over Jalal's crossbar.
Lee Frecklington passed up a glorious chance to make it 2-0 in the 72nd minute after firing over from the edge of Bournemouth's 18-yard box after Oakes' corner had been only half cleared.
Bournemouth manager Jimmy Quinn called on substitutes Mark Molesley, Sammy Igoe and Joel Ward for the closing stages but the home side never looked like forcing an equaliser.