It was a less happy day for San Lorenzo, whose coach Ramon Diaz resigned after a 1-0 defeat at Tigre.
Palermo's long run looked set to continue as he came close with three chances earlier in the match at the Duco, twice hitting the woodwork and having another saved on the line, before he tapped home fellow striker Pablo Mouche's square ball in the 83rd minute.
"If that last chance hadn't gone in, I'd have had to go," a relieved Palermo told Futbol Para Todos.
Boca climbed into 14th place in the standings of the season's second championship with 14 points, seven behind leaders Velez Sarsfield, who were upset 3-2 at home by relegation-threatened Quilmes on Saturday.
Palermo, Boca's all time record scorer, took his career tally in all top flight competitions including nine for Argentina to 301.
The Boca faithful were worried by Palermo's lack of goals as he runs down his career at the age of 37. He has eight matches left as he is retiring when the season ends in June.
"I assume full responsibility for what has happened. We have failed as a coaching staff and as everything depends on results I can't carry on in this situation," Diaz told reporters.
"I'm used to fighting at the top (of the standings) and we've lost our chances."
The Saints, who according to media reports tried to persuade Diaz to stay on at least until next weekend's "clasico" at home to Huracan, are mid-table with 15 points from 11 matches.
