Paul McCallum had given the O’s a half-time lead, though within 30 seconds of the restart substitute Charlie Wyke levelled.
A wonderful piece of individual skill from Harry Cornick put Orient back in front, and just as they looked like securing victory up stepped Grainger from the spot.
Orient kept faith with the side which won 2-1 at Morecambe last weekend, with the only change coming on the bench with the inclusion of second year scholar Henry Ocheing in place of Josh Koroma who missed out through illness.
It was the hosts who started on the front foot and they went closest to breaking the deadlock with six minutes on the clock as the ball found its way into the Orient box and defender Mark Ellis saw his close range effort strike the side netting.
Up the other end Gavin Massey did well to dispossess the Carlisle defence deep in their half before pulling the ball back for Paul McCallum. The striker took one touch to set himself before firing a fierce effort straight at goalkeeper Mark Gillespie.
The prolific Liam Kelly was then presented with another opportunity as the ball fell to him kindly 25 yards from goal. The midfielder advanced forward before seeing his strike go narrowly over the bar.
Both teams had settled into their stride well, with both teams trying to use long throw-ins to their advantage.
McCallum’s effort for the O’s was collected by Gillespie but up the other end on 23 minutes the ball fell to Michael Raynes and his left-footed effort was wide of the target as it remained goalless at the half way point of the first period.
The chance of the half though fell to that man Kelly as the ball was played wide to Massey who took a couple of touches before laying it into the path of the former Oldham man, but this time the midfielder couldn’t find the back of the net as he lifted the strike over the bar.
Carlisle went closer still on 31 minutes though as former O’s loanee Nicky Adams was afforded too much time on the ball 20 yards from goal and he curled an effort goalwards past the dive of Alex Cisak, but the post came to Orient’s rescue.
The O’s were under pressure, as Shaun Miller curled an effort goalwards which Cisak was equal to, and then moments later the same player should have got his head on a teasing inswinging cross from Jamie Devitt.
Orient weathered that spell and on their next foray forward a lovely ball in from Kennedy found the head of McCallum but the striker was unable to get the effort on target.
The visitors built on that and McCallum linked up with strike partner Bowery to present another opportunity, which Gillespie smothered behind for an O’s corner.
Orient were ending the half strongly and a lovely move a minute before the break saw the O’s break the deadlock.
Robbie Weir was heavily involved and his ball in to Bowery was played on to the advancing McCallum who shot low past the advancing Gillespie to give the O’s the lead.
Keith Curle opted to make two changes at the break for his side, with Wyke and Reggie Lambe both coming on in place of Mark Ellis and Jamie Devitt respectively.
And within a space of the opening minute that move had paid off when Wyke was on hand to slot home within 30 seconds of the restart as he slotted home at the back post from Shaun Miller’s ball in from the right.
That unsurprisingly lifted the hosts and the O’s were thankful for keeper Cisak just two minutes later as he superbly tipped over Adams’ fierce strike from 25 yards.
That spell of pressure from the hosts faded and McCallum’s long throws caused a few problems as one fell to Massey at the back post who teed it up for Weir, however, his strike was way over the bar.
Ollie Palmer had been brought on for Bowery, who appeared to pick up a slight injury in the first period, and was presented with an opportunity following some fine play by Cornick, however, he was unable to direct the headed effort on target.
Having weathered the storm the O’s pushed forward and put themselves back in front through a wonderful piece of individual brilliance from Cornick.
The Bournemouth loanee jinked his way in between several Carlisle defenders before firing low across goal past Gillespie to net his first goal for the E10 side.
Cornick was close to doubling his tally and the lead when he tried his luck from distance and his effort took a wicked deflection on its way behind for a corner.
Now behind, the hosts introduced former O Jabo Ibehre off the bench as they pushed for the equaliser, and Wyke found the side netting from a right-wing cross by Tom Miller.
Carlisle continued to push forward and they were awarded a penalty with just three minutes of normal time remaining when Kelly was adjudged to have handled a ball into box.
From the spot, Cisak went the right way but couldn’t get to Grainger’s powerful effort as the hosts drew level for the second time in the game.
Unsurprisingly Carlisle pushed forward for a late winner, but the O’s defence remained resolute to the death as they made the long journey back from Cumbria with a point for their efforts.
Carlisle United: Gillespie, Grainger, Joyce, Raynes, Ellis (Wyke HT), Jones, Adams, Gillesphey, Devitt (Lambe HT), Shaun Miller (Ibehre 70), Tom Miller.
Subs: Atkinson, Kennedy, Brough, Crocombe.
Goals: Wyke (46), Grainger (87’ pen)
Booked: Raynes (73), Ibehre (87)
Orient: Cisak, Kennedy, Parkes, Erichot, Hunt, Cornick, Kelly, Weir, Massey, Bowery (Palmer 51), McCallum (Semedo 78).
Subs: Sargeant, Nnomo, Pollock. Judd, Ochieng.
Goals: McCallum (44), Cornick (64).
Booked: Kelly (51), Kennedy (56), Hunt (90+5)
Attendance: 4,465 (236 Leyton Orient supporters)
Referee: Ben Toner