Jebbison slotted the ball past Jamie Head in the 67th minute - a goal that ended a run of five straight defeats in the league under the new management duo.
Despite the result, The Blues are still bottom of the division after Kettering Town won away to Bromsgrove Sporting.
Munn and McGugan made four changes to the side that faced Stourbridge in the Emirates FA Cup in the previous weekend. Ben Whiting made his debut in goal after signing from Stamford on Thursday and Lincoln City loanee Morgan Worsfold-Gregg started in midfield. Ed Cook replaced Keiran Walker at centre-half while Adam Clark came in for Zayn Hakeem, who was on international duty with Antigua and Barbuda.
In a cagey start to the match, United came out on top. Improvised centre forward Marley Fearon held the ball up well and carved out a chance early in the half as he brought down Whiting’a kick, turned past his man and shot - although the effort from distance was blocked.
Moments later Adam Clark had a great opportunity to put The Blues ahead. Lucien Mahovo found the run of fellow Notts County loanee Ryley Reynolds down the left, who cut the ball back to Clark who unfortunately could not hit the target as he ran onto the ball.
The hosts won corner after corner at the other end but Cook and Riece Bertram dealt with the threat comfortably.
Then, as Callum Cocks delivered a corner, the referee spotted a handball in the Berkhamsted box and awarded a penalty to United.
George Atwal stepped up to take the spot kick, which he blasted down the middle, however, Berko goalkeeper Jamie Head reacted quickly and saved the shot with a strong hand.
Goalless at the break, the hosts began the second half on the front foot. Berko passed the ball around nicely and worked a couple of great chances, although Whiting commanded his area well and made some crucial saves to maintain parity.
As the half progressed, United reclaimed control of the match. Mahovo marauded down the left, overlapped Clark and almost rounded the keeper after he won back possession in the final third but was denied by the bobble of the ball.
Jebbison broke the deadlock in the 67th minute and gave Long Eaton a well-deserved lead. Mahovo ran to the byline and cut the ball back across for Jebbison to fire past head.
Alans Voskresenskis came off the bench and almost had an instant impact. The young forward beat his marker for pace, cut inside and shot but Head made a strong save at the near post.
The Blues defended their one-goal-lead resiliently and in stoppage time a final chance to equalise fell to the hosts. Kyal Williams found space for the shot 18-yards out but fired the attempt over the bar.