After Chris Hackett's superb run from midfield created a chance for Gary Alexander to expertly volley home from 18 yards after 31 minutes, the home side never looked back.
Record Lions goalscorer Harris did not take much longer to register his first, poking home Millwall's second seven minutes later. And veteran Harris really shone after the break with two expert finishes in five second-half minutes.
When a crisp one-two with Alexander sent him clear after 68 minutes, Harris guided the ball home and then he sent the home crowd into raptures with a stunning right-foot volley into the top corner.
The Lions dominated early with burly midfielder Ali Fuseini coming closest in the 23rd minute when Jalal expertly tipped his long-range drive round the post.
Lee Bradbury poked a difficult chance over the bar four minutes before half-time but the Cherries did not look like scoring on a night that belonged to Harris.