Sabri Lamouchi's side had not won in five previous Sky Bet Championship games, but they made an encouraging return to form at the KCOM Stadium as their tired-looking opponents rarely threatened.
Forest's game management was particularly impressive – especially once Grabban scored an 11th-minute penalty.
Grabban then confirmed an away win when he smashed home from a tricky angle after 82 minutes.
This result was even more laudable as Hull had won their previous three home games. City also began purposefully in a bid to improve upon that record.
Indeed, the hosts should have gained a fifth-minute lead when Bowen's neat free-kick from the right caused unease within the Forest back-line.
Midfielder Jackson Irvine was quickest to react from the resulting skirmish, but he somehow fired over the crossbar from four yards with a stretching lunge.
If Irvine was frustrated by that miss, the Australia international's mind would have been even cloudier when he contributed to Forest's opening goal six minutes later.
An innocuous ball over the top was not effectively dealt with as Samba Sow, who later in the half hobbled off through injury, was afforded time and space to control inside the hosts' penalty box.
Sow was not in an especially dangerous position, though, and Irvine should have known better than to hastily react with a clumsy challenge.
Referee Geoff Eltringham pointed towards the penalty spot, from which Grabban battered the ball down the middle of the goal.
Hull supporters expecting a reaction were made to wait as Forest were the better side for the remainder of a scrappy first half.
Midfielder Alfa Semedo was a constant nuisance, while Grabban's movement was emblematic of Forest's dynamism on the counter-attack.
In deteriorating conditions, Forest continued to catch the eye after the restart.
And they might have added a second after 48 minutes as goalkeeper George Long, who was unsighted through a wall of players, did well to stop Tiago Silva's volley from the edge of the area with his feet.
Hull had their moments thereafter, but Forest goalkeeper Brice Samba was never once tested as a stop-start game meandered towards the final half-hour.
Whereas the home team laboured where it mattered, the visitors always had an outlet in Grabban, who was as intelligent in possession as he was lively on the break.
Seemingly out of ideas, Hull became increasingly dependent upon the long ball.
But one glancing Bowen header after 80 minutes aside, their efforts were too predictable and came to naught.
Forest substitute Ryan Yates should later have rubber-stamped an away win when he stabbed the ball wide following Joe Lolley's astute drag-back across the face of goal.
Yates' miss was irrelevant as Grabban added a second on the counter-attack with a fierce hit from the right of the penalty area following more good work from Silva.