Dion Charles scored twice, either side of an own goal from Liam Smith, with the points safely in the back pocket by the half time interval.
A third successive win in all competitions was accompanied by a third straight clean sheet – something Nathan Baxter had to work hard for with a fine save to deny Lewis Freestone midway through the second period.
Bolton were completely in control, however, rattling in 15 shots, seven on target, and keeping 74 per cent of the possession too.
Charles opened his account for the season with a smart finish, Adeboyejo playing a clever ball around the corner to his strike partner who passed the ball confidently past the prone Luke Southwood.
Wanderers are nigh on impossible to budget once they go in front but Evatt has often voiced his frustration that they do not go for the jugular when in such a position. For the next 20 minutes, they were as ruthless as it was possible to be.
The second goal came from a free kick on the left, given for an agricultural challenge from veteran Curtis Davies on Adeboyejo. Aaron Morley whipped in a dangerous ball to the near post where Kyle Dempsey and his hapless marker Liam Smith conspired to put the ball into the net.
Less than five minutes later it was three, this time there was no ambiguity about the scorer, with Charles finishing emphatically into the bottom corner after seizing on a sloppy defensive touch in the penalty box.
Cheltenham were fortunate to go back in at half time only three goals down, with Wanderers fizzing a few other efforts around Southwood’s goal.
At the opposite end, Nathan Baxter had little to trouble him. Rob Street hit one off-balance shot wide from a tight angle but the goal threat was coming entirely from the men in black.
With the points already in the bag would the Whites conserve energy for Fleetwood on Tuesday night? Or would Evatt urge his side to go on and do more damage?
Wanderers certainly showed intent. Morley hit the top of the bar with a looping cross, Morley and Dempsey had pot-shots from outside the box and Williams put a header over the bar.
Evatt was booked by referee David Rock for dissent and tempers flared again a few moments later after Cheltenham sub James Olayinka picked up an injury in a penalty box challenge with Josh Dacres-Cogley but the officials allowed play to continue. Home boss Wade Elliott was unimpressed that Bolton had not put the ball out of play – even after Evatt marched to the opposite dugout to make his case.
Baxter’s by-standing finally came to an end with a stunning fingertip save to push over Lewis Freestone’s header. He later came out to make another from Street after he had got the wrong side of Jack Iredale in stoppage time.