The Gills were disappointingly beaten with some ease, by a useful Wycombe outfit, definitely the best team I have seen in League Two this season.
Gary Waddock's side settled very quickly into the game and showed throughout why they were unbeaten away from home this season, looking dangerous every time they got forward.
Had it not been for the form of Gillingham keeper Alan Julian the visitors could have won far more comfortably.
Gillingham boss Hessenthaler made two changes to the team that started at Northampton on Saturday, Dennis Oli and Danny Spiller replaced Kevin Maher and Mark Bentley.
The game started in a lively manner with both sides seeming to find defending a struggle in the windy conditions.
The Gills had a first minute let off when Stuart Beavon broke down the right and drilled a low ball across the face of goal, just inches away from Kevin Betsy who was coming in at the far post.
In the fifth minute it was Beavon again who went through but this time Alan Julian was out quickly to block on the edge of the area.
A minute late Chris Palmer swung in a low cross from the left and Chris Westwood had a narrow escape as he got in front of Cody McDonald and headed against Nikki Bull's right-hand post.
Then a dangerous low left-wing cross from Betsy was clutched by Julian as Beavon looked to get a foot in.
Then as the clock ticked into double figures Adebayo Akinfenwa headed a Danny Spiller free-kick straight at Bull.
A Jack Payne throw was returned back out to him and the midfielders cross to the far post almost found Tony Sinclair and McDonald but the ball bounced off one of them into the hands of the keeper.
Akinfenwa then went close again, after breaking down the right side of the Wycombe defence he blasted his shot over the near post.
The next chance wasn't too long in coming, 18 minutes were on the clock when Spiller was off target with a shot following Palmer's ball in.
The visitors opened the scoring in the 23rd minute. The Gillingham defence was cut open again as Betsy and Beavon played their part in setting up the advancing Gareth Ainsworth who fired a low angled shot across Julian into the far corner.
In the 31st minute Akinfenwa battled for the ball in the visitors area but then saw his right-foot shot deflected wide.
Spiller found his way into refereee James Linington's notebook in the 32nd minute for a foul on Betsy.
Eight minutes before the break McDonald broke down the left-hand side of the Wanderers defence before firing across the face of goal.
It was the visitors who ended the half the better as first Ben Strevens fired over the top and Beavon had an air-shot with the goal at his mercy.
It took Wycombe just four minutes to increase their lead. Strevens short pass evaded Barry Fuller and Betsy strode on before firing home inside of Julian's near post.
As the Gills looked to hit back Jack Payne fired over the top and Palmer miscued another effort badly wide.
Just after the hour the Gills boss withdrew Akinfenwa and brought on young Ashley Miller for his debut. The youngster played wide on the right with Oli moving up to partner McDonald.
The move almost paid off immediately. A Payne cross was met by the diving McDonald but his header was scrambled away by Bull.
A series of corners quickly followed but the only effort saw Palmer shoot across goal.
In retaliation, Betsy fired a shot across Julian and Beavon forced Julian into a near post save after he shook off the attentions of Tony Sinclair.
Ainsworth then left Nutter trailing as he chased a ball over the top but Julian was again in the right place to beat away the veteran midfielders shot.
Julian was proving to be the Gills saviour as he then parried a fierce Danny Foster strike.
Payne became the second Gills player to receive a yellow card in the 70th minute for a foul on Westwood.
The second change brought some jeers from the Rainham End as Bruce Inkango replaced the hard working Palmer.
A block tackle from Matt Lawrence on Scott Davies saw Betsy inadvertently sent clear but as Julian came out to narrow the angle, the in-form winger dragged his shot wide.
The third and final throw of the dice saw Stefan Payne introduced for the tiring Oli with nine minutes remaining.
The next chance fell to the newly introduced striker, but his shot was blocked by Bull.
With the visitors content to run down the clock there were not too many chances late on and rather strangely, one of the loudest rounds of applause on the night was when the excellent Ainsworth was withdrawn in the final minute.
The result means the Gills have dropped to 20th in the League Two table and are now just two points clear of the bottom two.
Gillingham: Julian, Fuller, Lawrence, Sinclair, Nutter, Oli (S Payne 80), Spiller, J.Payne, Palmer (Inkango 73), McDonald, Akinfenwa (Miller 61).
Unused subs: Hawkes, Bentley, Maher, S Payne, Southall
Wycombe Wanderers: Bull, Foster, Westwood, Winfield, Sandell, Ainsworth (Rendell 90+3), Montrose, Davies, Betsy, Strevens, Beavon
Unused subs: Arnold, Bennett, Johnson, Murtagh, McCoy, McClure
Attendance: 4,076 (144 Wycombe)
Referee: James Linington
Assistants: Carl Fitch & Ashley Slaughter
Fourth Official: John Magill