Shamrock Rovers have opened up a four-point lead at the top of the SSE Airtricity Premier Division table, albeit having played a game more.
Jack Byrne got on the scoresheet, completing a 3-0 win at home to Sligo Rovers.
Cork City are up to fourth in the table as Conor McCarthy and Dan Casey struck to earn a first home league win of the season.
With Bohemians coming to Turner’s Cross having avoided defeat in their opening five games, this was a big test for John Caulfield’s side but, similar to last year’s FAI Cup semi-final against the same opposition, they were up for the game and showed their class when required.
City's opener came when Dáire O’Connor’s delivery of a corner hung under the crossbar, allowing McCarthy to attack the ball and head home from close range.
James Tilley, who came on for O’Connor after he departed with a dislocated shoulder just before half time, had an impact early in the second half.
It was he who was fouled for a free kick 25 yards out within five minutes of the restart and, when he rolled it to Casey, the defender’s swerving effort deceived Talbot.
Dundalk are up to second after Pat Hoban scored from the spot in a 2-0 win away to Derry City.
UCD have picked up a first win of the season, with Richie O'Farrell scoring twice in a 3-0 win at home to Finn Harps.
Aaron Drinan celebrated his call-up to the Ireland under-21 squad, scoring both of Waterford's goals in a 2-0 defeat of St. Pat's.
Shelbourne are the new First Division leaders on goal difference following a 3-0 win at home to Wexford.
Bray drop to second after losing 1-0 at home to Athlone Town.
Rob Manley scored a hat-trick as Cabinteely won 4-1 away to Drogheda, while Limerick were 3-1 winners over Cobh at Markets Field.