Needing a win with four tries, Ballina led Monivea 12-3 at the interval thanks to tries from Sam Liebezeit and Darragh Whyte with out-half Whyte also kicking a conversion.
Calum Quinn's try early in the second half all but secured the victory and although Monivea fought back to 17-10, Michael Allen's try gave Ballina the bonus-point win they required on an historic day for the club.
Connemara defeated Buccaneers 46-14 but will have to settle for second place.
Galwegians recorded a vital 24-3 victory over Ballinasloe to maintain their hopes of avoiding the relegation play-off. That result sealed NUIG's relegation and they will be playing in J1B next season.
Sligo took a huge step towards the league title on Sunday as they defeated Corinthians 16-5 to take top spot. Tuam's bonus-point 31-5 victory over Ballinrobe mean they are the only side who can catch Sligo now but they will need the new league leaders to slip up. The battle for second place and a play-off against the side who finish second bottom in J1A is between Corinthians and Tuam.
Elsewhere in the division, Creggs recorded an impressive 42-15 victory over the already relegated Ballyhaunis and Castlebar beat struggling Loughrea, who will face the losers of the J1C promotion play-off between Corrib and Dunmore.
Dunmore and Corrib will face each other in a play-off for a place in Division 1B later this month. Corrib beat basement side Claremorris 33-5 at the weekend and Dunmore eased past Carrick on a 31-7 scoreline. The other game in the league saw Portumna defeat Westport 12-8.
Claremorris will face the losers of the J2 play-off in a promotion/relegation play-off.
Connacht J1A League: Connemara 46-14 Buccaneers, Monastery Field; Galwegians 24-3 Ballinasloe, Crowley Park (NUIG relegated); Monivea 15-24 Ballina, Monivea RFC (Ballina crowned champions);
Connacht J1B League: Ballyhaunis 15-42 Creggs, Ballyhaunis RFC; Castlebar 17-12 Loughrea, Castlebar RFC; Sligo 16-5 Corinthians, Hamilton Park; Tuam 31-5 Ballinrobe, Tuam RFC;
Connacht J1C League: Corrib 33-5 Claremorris, Corrib RFC; Dunmore 31-7 Carrick, Dunmore RFC; Portumna 12-8 Westport, Portumna RFC;
J2 League Semi-Finals: OLBC P-P Ballina, OLBC; Oughterard P-P Corinthians, Oughterard RFC;