The starlet was instrumental in ensuring three points went the visitors' way, while the ex-Porto man laid on the goals
The newly-promoted outfit remain within two points of reigning Ligue 1 champions Paris Saint-Germain at the summit, with the win at Stade du Roudourou their fifth straight victory.
Coach Claudio Ranieri had to make do without star signing Radamel Falcao again, so named Martial in his starting line-up for the striker's fifth appearance of the season.
The striker wasted no time in repaying his trainer's faith, firing Monaco into a fifth-minute lead with a clinical finish past Guy N'dy Assembe after James Rodriguez waltzed through a crowd of defenders.
Guingamp defender Jonathan Martins-Pereira ensured his team faced an uphill task getting back into the match when he received his marching orders for a second bookable offence for handball.
Radriguez made the home side pay soon after when he delivered a pinpoint corner for Layvin Kurzawa to head home and double the lead.
Despite their advantage, the second period proved to be a nervy one for Ranieri's men, as Guingamp threw caution to the wind and attacked Danijel Subasic's goal relentlessly.
Veteran attacker Thibault Giresse came closest to ending the Croatian's run of four consecutive clean sheets via a couple of menacing free-kicks, as well as a shot that came off the post, but the visitors eventually held on to secure a vital win.
Monaco will host Valenciennes next Friday with the aim of catching PSG at the summit, given the French champions welcome third-placed Lille that weekend.