Basel, who will go into the third qualifying round of the Champions League next season, finished one point clear of old rivals FC Zurich who beat FC Thun 1-0 in their final game.
Zurich will also go into the Champions League qualifying rounds.
Basel's 14th Super League title was never in doubt after the league's top scorer Alexander Frei, who this year quit international football, put them ahead after six minutes with his 27th goal of the campaign.
Teenager Xherdan Shaquiri added the second in first half injury-time as he cut inside his marker and scored with a low shot inside the post.
Cameroon's Jacques Zoua headed the third nine minutes after halftime following a corner.
Former Bayern Munich midfielder Fink took over before the 2009/10 season and also led them to the Swiss Cup last season.
St Gallen, Switzerland's oldest club, were relegated after losing their final match 4-2 at Young Boys Berne to finish bottom of the table with 31 points.
It was an unhappy end to a season in which a group of local businessmen stepped in to save the club from bankruptcy.
Bellinzona, who started the day in last place, finished a point ahead of St Gallen in ninth spot thanks to a 2-0 win over Grasshopppers and will face a relegation play-off.
Neuchatel Xamax, bought two weeks ago by Chechen businessman Bulat Chagaev, survived by the skin of their teeth, a goalless draw at Sion giving them an eighth-place finish ahead of Bellinzona on goal difference.
Relegation would have been a huge blow for Chagaev who has promised to take the club into the Champions League.
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