The Argentine 'Final' championship match was played behind closed doors at Boca's stadium, renowned for its deafening atmosphere, after crowd trouble by fans during their "superclasico" against River Plate two weeks ago.
Boca had not won a league game in 100 days, since the opening weekend of the 'Final' championship of the season. Saturday's points lifted them to 17th in the standings with 13 from 14 matches.
Martinez struck three minutes after the interval and Boca defender Claudio Perez later prevented Colon from equalising with an overhead clearance on the line.
"To have won today brings us some calm," Boca coach Carlos Bianchi said. "A win can bring another win."
The victory should stand Boca in good stead when they play in front of a noisy full house at home to Newell's Old Boys in their Libertadores Cup quarter-final first-leg tie on Thursday.
It will be the first of three meetings in a week with Newell's, who are top of the table with 29 points after a 1-1 draw at Quilmes.
Newell's will host Boca at their Marcelo Bielsa stadium in Rosario in the championship next weekend and again in the second leg of their tie in South America's elite club competition the following Wednesday.
Striker Ignacio Scocco took his tally as the championship's top scorer to 10 when he put Newell's ahead after eight minutes at Quilmes.
Scocco, however, had a 31st minute penalty saved by Silvio Dulcich before Miguel Caneo equalised for the home side four minutes from time.
League title holders Velez Sarsfield, eliminated by Newell's in the Libertadores last-16 on Wednesday, lost 3-1 at Godoy Cruz.
"The team's elimination from the Cup was a hard blow and playing this match less than 72 hours later complicated us," said Velez coach Ricardo Gareca.
Velez, winners of the 'Inicial' championship in December, have had a poor 'Final' as they concentrated on the Libertadores and are one from bottom with 11 points from 14 matches.
However, they will not be worrying about relegation yet since in Argentina it is decided on teams' average points over three seasons and they are top of that table.