The victory gave Boca four points from three matches in second place in Group Four, five points behind leaders Fluminense after the Brazilians beat Venezuela's Zamora 1-0 in Rio de Janeiro.
"We're playing well, we're going to fight for it in the Cup and the (domestic) championship," Boca captain Juan Roman Riquelme told reporters.
"It was a very important victory, what we came looking for. The start got complicated with the goal through bad luck but we were able to turn it round with attitude."
It was the third match in eight days in which Boca fell behind in the opening 10 minutes after losing 2-1 to Fluminense last Wednesday and 5-4 to Independiente in the league on Sunday.
Arsenal, hosting the match at their Julio Grondona ground, went ahead after 10 minutes when Boca defender Clemente Rodriguez turned a low cross into his own net.
But the visitors equalised just before the half-hour when winger Pablo Mouche latched onto a half clearance in the box and shot under goalkeeper Cristian Campestrini's dive.
The Argentine champions sealed the points in the 68th minute when Rodriguez crossed from the left and with two defenders keeping a close eye on burly striker Santiago Silva, substitute midfielder Pablo Ledesma ghosted in through to tap home.
Striker Luciano Leguizamon squandered an easy opportunity right in front of goal that would have given Arsenal a late equaliser.
Boca needed the win not only to stay in the hunt for a seventh title in South America's elite club competition but also to put behind them a week in which their home defeat by Fluminense was their first in 37 matches.
Mexico's Cruz Azul retained the Group Six lead with a 0-0 draw at home to second-placed Corinthians in Mexico City. After three matches Cruz Azul have seven points and the Brazilians five.
Libertad of Paraguay stayed top of Group Five after a 1-1 draw with Brazil's Vasco da Gama in an ill-tempered match in Asuncion. The same two players who scored the goals, Vasco's Diego Souza and Jose Nunez of Libertad, were sent off.
