Paul Groves’ men had most of the early pressure, and Marc Pugh opened the scoring for the Cherries after being played in by Joe Partington.
Josh McQuoid and Matt Tubbs were a constant threat in the first-half, and had a number of chances between them before McQuoid slotted home just before the break.
Tubbs made it three soon after the restart, before an own goal and a goal from substitute Alex Moth put the Cherries out of sight.
Delano Sam-Yorke pulled one back for the Dragons but the Cherries were certainly deserving of their 5-1 win.
Dragons’ striker Tim Sills threatened for the hosts early on with a header which flew wide, before Cherries’ midfielder Joe Partington skied an ambitious long-range shot.
New signing Eunan O’Kane had his first impact in a Cherries shirt when he skilfully played in Tubbs, but the ex-Crawley man was offside.
A minute later, Pugh came inches away from opening the scoring when he deftly cut inside before being denied by the crossbar.
But the early pressure was rewarded after 22 minutes when Partington played an inch-perfect through ball to Pugh, who shot past ‘Stoke goalkeeper Bayes to take the lead.
The Dragons nearly made an instant response when Nathan Smart crossed for Sills, but his header was again missing the target.
With ten minutes left of half-time, McQuoid and Tubbs involved in a series of chances for the Cherries. McQuoid first forced Bayes to make a finger-tip save from a free-kick before setting up Tubbs who shot straight at the ‘keeper.
McQuoid then smashed the crossbar after some great play, before finally getting the goal his pressure deserved.
The lively O’Kane found space down the left before playing in the former Millwall striker, who made no mistake this time with a composed finish just before the interval.
It took just two minutes into the second-half for the Cherries to extend their lead. This time Pugh turned provider and played in Tubbs who made it three.
Former Bournemouth trialist Jordance Holder-Spooner came close to reducing the deficit, but after rounding the ‘keeper with players back on the line, he skied over the bar.
Shortly before the hour-mark, Dragons forward Stuart Lake force Shwan Jalal into a solid save.
With 25 minutes left, Pugh made it 4-0 to the Cherries after forcing an own goal from the unlucky Basingstoke defender Smart.
Two minutes later, and substitute Moth made it five. After some great link-up play, the youngster got hold of the ball and calmly slotted home.
Substitute Jayden Stockley came close to scoring with his first touch after a fierce free-kick, before Dragons’ sub Toby Little kept Jalal on his toes with a ferocious effort.
Sam-Yorke gave the Basingstoke fans something to cheer about when he lashed home with ten minutes left, and 5-1 was how it finished at the Camrose.
Dragons: Bayes, Smart, Rice, Warner, Adams, Gasson, Lake, Daly, McCauley (Dunn 67), Sills, Holder-Spooner (Sam-Yorke 63).
Goals: Sam-Yorke (84)
Cherries: Jalal, Bowles (Cargill 75), Zubar, Barrett (Strugnell 65), Daniels (Wakefield 75), McDermott, Partington (Stockley 75), Arter (Gilkes 75), Pugh (Jamal 75), McQuoid (Moth 45), Tubbs (Makoni 75).
Goals: Pugh (22) McQuoid (43) Tubbs (47) Smart O.G (65) Moth (67)