The former Millwall man grabbed all the goals for the O's and although Bradley Dack gave the Gills hope late on it proved to be nothing more than a consolation goal as Orient ran out 3-1 victors at Priestfield and continued their sensational start to the season.
Orient manager Russell Slade made four changes from the side that had beaten Colchester at the weekend with Johnny Gorman, Marvin Bartley, Batt and new loan signing Jayden Stockley all coming into the O's starting XI for the trip to Kent.
The game had started in conservative fashion and it took until the 11th minute for the first real chance of the match to be created. Nathan Clarke's weak header back to Jamie Jones was nearly seized upon by the onrushing Cody McDonald but the O's stopper was quick off his line to avert the danger and collect.
It had been a scrappy start to the evening with both sides adopting a very direct approach and the ball rarely leaving the air. Despite only signing for the club yesterday from AFC Bournemouth, Stockley was right in the thick of the early action and was linking up well with Batt at the top end of the pitch.
After failing to create anything in the opening stages, the O's were gifted the chance to take the lead in the 25th minute. Romain Vincelot was clumsily fouled in the area by McDonald and referee Michael Bull didn't hesitate in pointing to the spot to award the O's their third penalty of the season. Batt stepped up and confidently sent ex-Orient goalkeeper Stuart Nelson the wrong way from 12 yards to give Orient the lead and grab his first goal of the season.
Martin Allen's side responded well to the O's goal however and Orient skipper Clarke helped keep the score in Orient's favour with two fantastic blocks to deny Antonio German and Cody McDonald. McDonald then had an even better chance to draw the Gills level just moments later as the forward was set racing through on goal only to see his shot fly just wide of the target from inside the area.
The O's rode the brief wave of pressure from the visitors and then managed to double their lead on the stroke of half-time. Moses Odubajo was set free down the right hand side and the winger tormented Joe Martin before delivering a fantastic cross which was met by Batt who struck home from six yards. The two goal lead flattered Russell Slade's side at the break and the O's somehow found themselves 2-0 up having failed to create any other chances in a predominantly uneventful opening half.
The second period started in very much the same vein as the first but the O's were just edging proceedings as they looked add some extra gloss to the fortuitous winning position they found themselves in. A fine pass from Vincelot set Johnny Gorman free in the area but the winger's fizzing cross just evaded the Orient contingent that occupied the penalty area.
However the O's would go on to add a third goal on the hour mark. Stockley and Batt linked up well again and Batt easily beat Leon Legge before rolling the ball past Nelson and into the bottom corner of the net to complete a well-taken hat-trick.
The goal looked to have really deflated the home side but against the run of play the Gills grabbed themselves a lifeline with 20 minutes left. Bradley Dack ghosted in at the back post to head home from close-range although Jamie Jones was convinced that Dack was in an offside position and was booked as he aired his frustrations to the linesman.
Dack's strike would prove to be a false dawn for the Gills however as they failed to create any other chances in the closing stages and the O's comfortably progressed to the second round of the competition.
GILLINGHAM LINE UP: Nelson, Martin, Legge, Whelpdale (Weston, 67), McDonald, Gregory (Allen, 45), Dack, German (Kedwell, 74), Hollands, Harriman, Barrett (C)