A second half strike from Daniel Butterworth sent Rovers through to the fourth round of the FA Youth Cup.
The Academy top scorer bagged his eighth goal of the season 12 minutes from time as Rovers got the better of Arsenal.
In a feisty encounter at Meadow Lane, the Gunners were reduced to ten men after 22 minutes when Reiss Nelson saw red for a clash with Joe Rankin-Costello.
But despite the man advantage, it wasn't until 78th minute that Billy Barr's were finally able to make it count. Lewis Thompson crossing from the left to where Butterworth blasted home from close-range.
Arsenal could have sent the game into extra-time, but substitute Nathan Tella fired wide from 12-yards with the last kick of the game.
The Gunners fashioned the first chance of the game after just six minutes at Boreham Wood. Working the ball well down the right Donyell Malen crossed to the near post but striker Eddie Nketiah lashed narrowly wide.
Rovers responded well with three chances to grab the opening goal. Midfielder Jack Evans showed good awareness to pounce on a loose ball before feeding Daniel Butterworth, but the striker saw his left-footed shot diverted behind.
Rankin-Costello took the resulting corner from the right, hitting it deep to the back post to pick out captain Tyler Magloire but his header was claimed by Joao Virginia in the Arsenal goal.
Rovers were then inches away from taking the lead on 16 minutes as Lewis Thompson's header saw Rankin-Costello stretch for the ball, but it ran agonisingly wide of goal.
But the game then took a sour note at the midway point when Rankin-Costello and Arsenal attacker Reiss Nelson clashed sparking unsavoury scenes. After deliberation from the officials, referee Darren Knox issued a straight red to the Arsenal youngster and a yellow to Rankin-Costello.
Despite having the extra man and seeing more of the ball, it was the hosts carried the threat. Ben Ascroft had to dive to keep out a shot from Malen, before he watched an effort from Nketiah flash past the post.
Rovers ended the half on the up but without success in front of goal. Stefan Mols with a lovely turn and shot that deflected behind. Lewis Thompson's corner picked out Matty Makinson but he scooped the ball over the bar.
Both sides had half-chances as the second half got underway, but Rovers spurned a great opportunity just before the hour mark. Tre Pemberton's driving run took him past two defenders but his shot ricocheted off the legs of keeper Virginia and away to safety.
Butterworth then had sight of goal as the ball broke to him on the corner of the area, but his near-post shot went wide.
Another chance went begging soon afterwards as Arsenal's Nketiah turned well on the edge of the box, but his strike didn't trouble the Rovers goal.
But as talk of extra-time started to be muttered by the Boreham Wood crowd, it was Rovers who struck the decisive blow 12 minutes from time.
Left back Thompson did well on the overlap and as he sent the ball into the box, Butterworth was on hand to slam home.
That sparked late pressure from the home side as they looked to get back on level terms. Defender Joseph Olowu heading a free-kick wide on 89 minutes as nerves started to increase amongst the young Rovers.
But with all of the added time played there was still one last chance for the Gunners, but as the ball dropped to Nathan Tella 12 yards out, the substitute fired wide.
That proved to be the last kick of the game as Rovers celebrated their progress through to a fourth round home tie with Aston Villa.
ARSENAL: Virginia, Osel-Tutu, Bola, McGuane, Olowu, Da Silva, Smith Rowe (sub Tella 67 mins), Dragomir, Nketiah, Nelson, Malen (sub Willock 79 mins).
Subs not used: Pileas, Barden (GK), Coyle.
Off: Nelson 22 mins.
ROVERS: Ascroft, Jackson, Makinson, Magloire, Thompson, C. Doyle, Evans, Mols, Pemberton (sub Steer 85 mins), Rankin-Costello, Butterworth.
Subs not used: Campbell (GK), Lynch, Buckley, Wright.
Goals: Butterworth 78 mins
Booked: Rankin-Costello 22 mins, C. Doyle 83 mins, Makinson 90+5 mins.