The Hatters had taken the lead in the 17th minute through Michael Spillane only to be pegged back in the 51st minute after John Grant's leveller.
But after Ricky Newman was sent off for the visitors in the 78th minute, the hosts pressed and secured a first home league win thanks to Hall and Martin.
Luton should have gone ahead in the second minute when new loan signing Marc Pugh's cross from the left bounced off Anthony Straker into the path of Sam Parkin, but the former Chelsea man could only lob wastefully over from six yards.
Shots keeper Nikki Bull pulled off a stunning save four minutes later, diving full length to tip Rossi Jarvis' rasping 30-yard volley over the crossbar and was well placed to hold George Pilkington's header from the resulting corner.
For all Luton's threat they almost fell behind in the 11th minute when Louis Soares' knockdown fell to Anthony Charles, who scuffed against the foot of the post from eight yards.
Bull then parried Parkin's 18-yard drive in the 15th minute before Luton deservedly took the lead two minutes later as Spillane slid in to convert Jarvis' driven right-wing cross from six yards for his first ever Hatters goal.
The game was comically held up for nine minutes in the middle of the half after Keith Keane's wayward shot dislodged a fascia board on the Oak Road stand and stewards had to collect a ladder to remove the item.
Aldershot brought on Kirk Hudson for Scott Donnelly and the substitute almost had an instant impact when he ran on to Grant's flick in the 38th minute and forced a smart save from home keeper Conrad Logan.
Luton rallied and almost made it 2-0 in the third minute of stoppage time when Charles cleared off the line from Parkin's header after a superb cross on the right from Claude Gnakpa.
Hudson showed his threat again in the eighth minute of added time when he ran clear on to Soares' pass, but lobbed over from 15 yards with just Logan to beat.
Aldershot improved in the second period and drew level in the 51st minute when a simple long ball from Soares caught out the home defence and allowed Grant time to lift his shot over Logan from 16 yards for his first of the season.
The visitors could have gone ahead two minutes later when a quick break saw the Shots five against three, but Logan pushed Junior Osborne's 18-yard drive over the bar.
Aldershot brought on Scott Davies for Osborne in the 62nd minute and again the substitute almost made an immediate impact when he volleyed just wide from the edge of the area with his first touch.
Lewis Emanuel saw his mis-hit cross come back off the crossbar in the 73rd minute and five minutes later Aldershot were reduced to ten men when Newman saw red for his fierce challenge on Jarvis.
Luton pushed on and Hall nodded home from eight yards two minutes from time after meeting Gnakpa's cross from the right.
There was still time for another as Gnakpa again crossed from the right for Parkin to head into the path of Martin, who swept home in the fourth minute of stoppage time.