Cameron McGeehan put the Hatters in front with a tap in, before Danny Hylton doubled their lead.
Palmer pulled a goal back with just over 10 minutes to go, but it was to prove in vain as Orient lost out.
O’s boss Alberto Cavasin made three changes to the side which lost 1-0 last weekend against Portsmouth with Nigel Atangana, Ollie Palmer and Sandro Semedo all returning to the starting line-up in place of the injured Liam Kelly, Paul McCallum and Ulrich Nnomo respectively.
Chances were few and far between in the opening 10 minutes as both sides settled into the match, though a fine Yvan Erichot clearance denied Danny Hylton a goalscoring opportunity.
Orient were soon on the front foot and the first chance fell to Sandro Semedo as his fierce cross almost crept in at Christian Walton’s near post, though the on-loan goalkeeper was able to keep it out.
The O’s built on that and were close to breaking the deadlock when a fine cross from captain Nicky Hunt found its way to Palmer at the back post but he directed his header just wide of the target.
Up the other end, a cross from Alex Gilliead had O’s goalkeeper Alex Cisak at full stretch, however the attempt landed on the roof of the net.
A quick free-kick almost worked to good effect for the visitor as the ball in found the run of McGeehan and his shot on the turn was well kept out by Cisak.
The visitors remained in the ascendancy and on the half hour mark they took the lead. Jay Simpson was dispossessed in midfield and the ball fell to Marriott who saw his initial shot saved well by Cisak, however, McGeehan was on hand to tap home from close range.
The O’s rallied from that and the ball fell to last season’s top goalscorer Simpson in the box but he was just unable to clear sight of goal as his shot was blocked.
Marriott created, and almost finished, the Hatters next attempt as he received the ball out wide on the left before coming inside and only a Parkes deflection kept the effort at bay, while when the O’s foraged forward, Semedo’s weak effort was comfortably held by Walton.
Palmer’s initial free-kick minutes later struck the wall before his follow-up was deflected wide for a corner and that proved to be the final action of the first half.
No changes were made at the break by either side and the opening chance fell to Atangana as his shot flew well over the bar, before Simpson tried his luck moments later and was also off target.
It was a strong start for the O’s and Simpson was just unable to get on the end of a teasing delivery from Semedo as they continued to push forward
The Hatters went closer still when Marriott’s effort was tipped onto the post by Cisak, before Jordan Cook tried to race on to the loose ball, however, the Aussie stopper was there to get a decisive touch and the danger was cleared.
Nicky Hunt, not known for his prolific goalscoring record, almost notched his first for the O’s when he rampaged forward but his effort was deflected into the side netting, before Semedo saw an effort held by Walton.
Simpson was replaced by Paul McCallum at the halfway point of the second half and he made an immediate impact as he dispossessed O’Donnell in order to tee up strike partner Palmer who got a shot away however Walton was equal to the strike.
Despite the pressure from the O’s it was the Hatters who were to double their lead when a lovely throughball found Marriott and though he was unable to get a shot away he played it into the path of his strike partner Hylton who finished with aplomb.
Their two-goal cushion didn’t last long though as McCallum played the ball back into the path of strike partner Ollie Palmer on 79 minutes, and his effort trickled over the line off the inside of the post to give the O’s a lifeline.
Cisak went on to deny Hylton’s fierce effort as the game entered the final five minutes of normal time and despite five additional minutes at the end of the game, the O’s were unable to force a late equaliser.
Orient: Cisak, Hunt, Erichot, Parkes, Kennedy, Massey, Atangana (Dunne 75), Janse, Semedo, Simpson (McCallum 68), Palmer.
Subs: Sargeant, Nnomo, Bowery, Pollock, Benedicic.
Booked: Semedo (80)
Goal: Palmer (79)
Luton Town: Walton, O’Donnell, Cuthbert, Sheehan, Potts, Rea, Cook (Mullins 90), Gilliead (Gray 90+2), McGeehan (Smith 83), Hylton, Marriott.
Subs: King, Ruddock, Vassell.
Booked: Hylton (80)
Goals: McGeehan (30), Hylton (75)
Attendance: 5,471 (1,341 Luton Town fans)
Referee: Trevor Kettle