Summer arrival Guirassy got on the scoresheet alongside captain Emre Can, who scored a penalty, and Felix Nmecha.
Dortmund now have ten points from five games while Bochum are one of three Bundeslinga outfits, alongside St Pauli and Holstein, on a single point.
Dortmund came into the match with their local rivals stung by a 5-1 thrashing at the hands of Stuttgart last week for their worst start to a league season since 2014-15, when then manager Jurgen Klopp stepped down from the club.
The hosts started brightly against a Bochum side yet to win in any competition this season but were behind after 16 minutes, Matus Bero scoring on the counter against the run of play.
Just five minutes later, the home side were two down after a poor attempt to play out from the back laid the ball on a platter for Dani de Wit to slam home, giving Bochum a 2-0 lead after 21 minutes.
Dortmund coach Nuri Sahin cradled his head in his hands while former manager Edin Terzic, who took the club to last year's Champions League final, watched on in the crowd.
Shellshocked, Dortmund failed to spark to life and Bochum could have had a third when Monaco loanee Myron Boadu broke free on the counter but scuffed his shot wide.
With Dortmund reeling, Guirassy struck just before half-time, heading in a Julian Brandt cross to draw the hosts closer at the break.
Guirassy's movement troubled the visitors and he won the hosts a penalty after 61 minutes, going down in the box under attention from former Dortmund defender Felix Passlack.
Can converted to draw the hosts level. After Sahin made four changes, Guirassy put the hosts in front with 15 minutes remaining, sliding a Karim Adeyemi pass under Bochum 'keeper Patrick Drewes.
Drewes could have done better from Guirassy's shot but made a meal of Dortmund's next attempt six minutes later, letting a Nmecha shot squirt under him to give the hosts control.
Guirassy now has four goals in his last three games for Dortmund, while Bochum sit second last in the table.
On Saturday, reigning champions Bayer Leverkusen travel to Bayern Munich.
