Atletico Madrid's surprise defeat at Athletic Bilbao gave Barca the chance to stretch its advantage at the summit going into the final international break of the season.
Messi scored twice in the first half at the Benito Villamarin, his first an unstoppable free-kick and his second coming moments before the interval, with Luis Suarez - who hurt his ankle late on - adding a third after the break.
On the day Messi drew level with Andres Iniesta on 674 appearances for Barca, the captain moved ahead of Xavi to set a new club record for featuring in wins - this victory becoming his 477th.
And after Loren Moron's late consolation for Betis, Messi capped his latest record with a wonderful third goal to add yet another match ball to his collection.
Messi, sporting a trimmed beard, opened the scoring with a typically perfect free-kick.
Arthur was bundled to the ground on the edge of the D and Messi beat former Espanyol goalkeeper Pau Lopez with a stunning strike from the resulting set piece.
Lopez then saved another Messi free-kick from slightly further out before Arthur's fine interception prevented a Betis equaliser.
Suarez shot tamely at Lopez when presented with a great chance by Messi but the duo combined for the Barca captain's second goal on the stroke of half-time.
Suarez's sensational back-heel pass was perfectly placed into the path of Messi, who was never going to miss, and Barca made certain of their victory in the 63rd minute.
The striker had just drilled a great chance wide, taking out his frustration on the advertising boards, but Suarez got his name on the scoresheet with a fine finish after a dazzling solo run.
Loren scored a late consolation for Betis after a pass from fellow substitute Diego Lainez, but Barca's lead atop LaLiga increased and Messi was left to celebrate another record after completing his treble with a outrageous chip that clipped the crossbar as it beat Lopez.
He even hit the post in stoppage time, by which time Suarez was limping heavily.