Missed chances cost Chesterfield three points in John Sheridan's first home game in the National League.
The Spireites were held to a 0-0 draw by Ian Evatt's Barrow, who finished the game with ten men after a late red card for Lee Molyneux.
Had Lee Shaw and Marc-Antoine Fortune not squandered first half chances, Sheridan might still boast a perfect record as Town boss.
As it is, he's yet to see his side concede a goal and they're now just a point from safety.
They could have been ahead as early as the third minute, Jerome Binnom-Williams' beautiful cross from the left finding Lee Shaw, who got the header all wrong and missed the target.
It was a very bright start from the hosts, who broke down the right through Shaw and when he found Jonathan Smith in the area, it took a vital block from Dan Jones to ensure the shot went wide.
Life for the visitors was made difficult in the early stages as the Spireites pressed them, stopping the passing game at source and forcing Barrow to go long.
That pressing forced a turnover of possession in the middle, Kiwomya countering with pace before Curtis Weston saw a low, hard shot well saved.
Another chance, a golden one, presented itself to Marc-Antoine Fortune who ran onto a long ball, went one on one with Joel Dixon but waited too long and the keeper was able to save with his feet.
In response, Barrow mustered a Jacob Blyth shot from distance that was comfortably held by Shwan Jalal.
The game then went through a scrappy phase, Chesterfield guilty of trying to force play on a number of occasions and simply wasting possession.
With six minutes to go in the half Town were forced into a change, Fortune coming off holding his hamstring, Tom Denton taking his place.
Barrow began to enjoy better spells, particularly on the counter attack, but having threatened to cut Town open a couple of times, let themselves down with the final ball.
The second half was 15 minutes old before there was anything in the way of excitement.
Again, it was Chesterfield who came close to scoring, Shaw's dinked cross flicked on by Will Evans, then nodded goalward by Denton, Barrow forced to clear off the line before Kiwomya's follow up header was blocked.
Denton had another pair of headers in quick succession, one deflected wide, another held by Dixon.
Barrrow finally unlocked the home defence with a quick passing move on the edge of the box and Evans had to throw himself in the way of Blyth's shot to keep the scores level.
The visitors suddenly looked a real threat and Jalal was twice called into action.
First he got down to stop a shot from an acute angle, then he hared off his line to dive at the feet of Jack Bartrum, before leaving his area to make two vital sliding challenges and clear the danger.
Both Hollis and Smith made crucial blocks to deny Jack Hindle and Angus, then Jones, unmarked at the back stick, powered a header wide of goal.
Chesterfield needed to relieve the pressure and a stirring run up the flank by Shaw did just that, the ball finding its way to Weston whose shot was deflected up and over Dixon's crossbar.
Referee Tom Reeves was in the spotlight twice in as many minutes, late on.
He said no to Weston's vehement penalty appeals, after a coming together with Dixon who had just spilled a cross, and then he gave Lee Molyneux his marching orders.
Molyneux had already been booked for a late challenge on Shaw when he steamed into the winger again on the touchline, with the outcome inevitable.
Try as they might, Chesterfield couldn't find the necessary quality to create a final, decisive chance and 10 man Barrow ended the game on top, winning a pair of corners but failing to grab a winner.
Chesterfield: Jalal, Barry (Rowley 48), Binnom-Williams, Evans, Hollis, Smith, Weir, Weston, Kiwomya (Reid 74), Shaw, Fortune (Denton 39). Not used: Beestin, Anyon.
Barrow: Dixon, Jones, Elsdon, Hird, Bartram, Molyneux, Taylor, Kay (Rooney 61), Turner (Hindle 61), Angus, Blyth (Brown 88). Not used: Wade, Granite.
Yellow: Blyth 57, Taylor 59, Molyneux 74, 83
Red: Molyneux 83
Referee: Tom Reeves.
Attendance: 4,626 (279 away)