Jack McMillan's first goal in three years was the opening goal.
Livingston ended a six-game winless run with a much-deserved victory as the alarming Scottish Premiership slump continued.
Jack McMillan's goal gave the hosts a 16th-minute lead.
After going down under a soft challenge, Martin had the chance to equalise from the spot, but he missed.
In the second half, the visitors were rarely threatened.
Jack Ross' men have just one win and seven defeats in nine league games. They are now 11 points behind third-place Hearts.
The win puts Livingston in ninth place, which puts them five points clear of Ross County, who have played two games fewer.
Reaction as it happened.
Hibs moved to a 4-2-3-1 formation after Chris Cadden was left out of the starting line-up.
The switch helped the visitors early on, as full-backs McGinn and Doig were always options on the overlap, while Josh Campbell was catching the eye playing behind Kevin Nisbet.
The away side were piling on the pressure as Jamie Murphy had a headed attempt cleared off the line before the winger crossed for Nisbet, who saw another headed attempt go straight into the arms of Max Stryjek.
The right-back flashed his strike wide when Craig Sibbald's fine reverse ball found him marauding forward, but Hibs left gaps at the back and were almost punished when they were without a clean sheet.
The hosts made no mistake when Andrew Shinnie on the left found the former Hibs man, who calmly tucked the ball under the pressure.
The home side's good work was almost undone two minutes after they broke the deadlock, when hesitant defending allowed Boyle to get into the box.
The Livingston players were incensed that the Australia international went to ground too easily.
The home crowd was happy when the penalty was scored.
After a couple manic minutes, Hibs were rattled and almost shipped a second when a side-foot finish by Sibbald was directed wide of Matt Macey's goal.
Hibs failed to get back into the game in the first half and the home side appeared to be galvanised.
Ross threw on Christian Doidge and Scott Allan to try and get back into the game.
Livingston got more joy in attack as Nisbet and Allan directed opportunities off target.
The home side wanted Hanlon to be sent off for a straight red card when the Hibs defender wiped out Shinnie, but the centre-back got away with a yellow.
It looked like Ross' side were playing with a man down for most of the second half as Alan Forrest ran riot.
The Livingston winger had a strike saved by Macey, before a dangerous cross was clawed away either side of the substitute's effort that dropped just past the far post.
McGinn was shown a second yellow card for a tug on Montano, which made Hibs' second-half performance look like they were a man short.
Hibs captain Hanlon was also dismissed after another booking for hacking down Forrest.
Even though Ross' men had nine men, they almost snatched a point when Nisbet's poor finish was off target.
Stephane Omeonga was the man of the match.
The ex-Hibs player was a star against his former club, snapping into challenges and driving his side with an inspiring display.
What did we learn?
A lot of cracks at Easter Road have been papering over by Hibs' League Cup win over Rangers. That is a head-scratcher, given how well Ross' side played that day.
The Hibs boss would have been hoping that the victory would act as a wake up call.
If Ross's side are to regain any kind of form before next Sunday's final, they will have to play away and at home.
The Leith side's failures can't take away from how good Livingston were. A defeat for Martindale's men would have left them two points behind County, who are picking up form, and they have two games in hand.
The Livingston boss needed a positive result and performance to be good.
What's next?
Hibs and St.Mirren are both playing on the same day as Livingston faces a trip to Dundee United.
Livingston
Hibernian
Line-ups.
Match statistics.
Live text.
Formation 4-3-3.
2Devlin5Fitzwater4Parkes
21McMillan18Holt33Omeonga
10Sibbald22Shinnie17
The book was written at 17 minutes.
2Devlin.
5 Fitzwater.
Substituted for Obileyeat 45' minutes.
The book was written at 50 minutes.
Substituted forPittman at 67' minutes.
18Holt
Booked at 49 minutes.
Substituted forMontao at 59' minutes.
Shinnie.
17 forrest
Substitutes.
6Obileye.
8Pittman.
9 Anderson.
11Montao
15Panayiotou
24 Kelly.
36 Maley.
Formation 4-2-1-2.
6McGinn5Porteous4Hanlon3Doig
10Boyle22Doyle-Hayes11Newell18Murphy
1Macey
Booked at 85 minutes.
Substituted forMcGregorat.
The book was written at 89 minutes.
3Doig
10 Boyle.
The book was written at 55 minutes.
11Newell
Murphy replaced Allanat 45' minutes.
Substituted for Doidge at 45 minutes.
15Nisbet.
Substitutes.
9Doidge.
13Gogic
Stevenson is a person.
21Dabrowski
Allan
24McGregor
25Scott.
The match ended with Livingston defeating Hibernian 0.
The second half ended with Livingston defeating Hibernian 0.
An attempt was missed. Kevin Nisbet's shot from the centre of the box is wide to the left.
Foul by Kevin Nisbet.
Scott Pittman won a free kick in the defensive half.
The second yellow card was for a bad foul.
Foul by Paul Hanlon.
Alan Forrest won a free kick.
The attempt was saved. The left footed shot from the left side of the box is saved in the top left corner. Scott Pittman assisted.
The attempt was saved. Alan Forrest's left footed shot from the centre of the box is saved in the bottom left corner. Scott Pittman assisted.
Paul McGinn was given a second yellow card for a bad foul.
Foul by Paul McGinn.
The attacking half has a free kick.
The substitution was for Hibs. Ryan Porteous was replaced byDarren McGregor.
Corner in Livingston. Paul McGinn was in the match.
The attempt was saved. The shot from the left side of the box is saved in the bottom left corner. Joe Newell assisted with a cross.
Corner, Hibernian. Stephane Omeonga Conceded.
The defensive half is where Joe Newell won the free kick.
Foul by Scott Pittman.
Corner in Livingston. Jake Doyle-Hayes was in the match.
