The Mariners held on to a slim 9-8 edge in the early stages of the contest. Mikos and Joe Sheehan paced the Bears (0-2) to an eight-point advantage, the largest of the game, with eight minutes to play in the first half, 25-17.
With 66 seconds left in the period, Mitchell came to within a point, 31-30, but SJC took a 35-32 lead into the break.
The Bears went back and forth with the Mariners for much of the second stanza while holding on to their lead for much of the period as Mikos, St. Francis Prep product Evan Sirakis, and Archbishop Molloy alum James Mojica of South Ozone Park combined to go 14-24 from the field.
Mitchell's Jalen Benson banked a pair of free throws with 6:35 on the clock to take a lead that they ultimately never surrendered, 63-61.
However, the Bears trailed by as little as one with six seconds remaining in regulation thanks to a Sirakis three-pointer to make it 79-78 before Alfonso Stokes' shots from the line with two seconds to go gave the Mariners third place at the ECSU Tournament.
Sirakis scored 16 points on 7-of-12 shooting and registered three assists and a steal, while Mojica and Sheehan each went for 10 points and six rebounds.
The Bears return to Brooklyn on Thursday as they begin their Skyline Conference slate against nationally ranked Yeshiva University in their home opener. Tipoff from The Hill Center is scheduled for 7 p.m.