The winner was scored in the 25th minute of the game by Marines' Australian recruit Troy Sutherland with a grounder from the top of the circle.
The victory for Mumbai was their first in two games, following the 5-7 defeat to Pune Strykers in a rip-roaring opening clash at the same venue on Thursday.
The Badshahs had come into the game following a 4-3 victory over Chandigarh Comets on February 29.
Friday's match was played at a much slower pace than the opener between Mumbai and Pune Strykers. The Marines looked a wee bit slow initially which was taken advantage of by the Badshahs who made initial forays into the rival area.
Goalmouth thrills were also few and far in between, in sharp contrast to Thursday evening's encounter when it rained goals and the pace was electric.
Both teams also lacked effective drag-flickers to take advantage of the few penalty corners awarded.
While Mumbai forced three short corners, their rivals earned six, but both teams were ineffective off these set-pieces due to poor conversions.
Bhopal did the running in the initial stages of the tie and could have gone ahead in the 9th minute but for Mumbai captain and custodian Adrian D'Souza bringing off a good save.
Former international Sameer Dad and Affan Yusuf strung a move on the left of the mid-field before the latter essayed a stiff shot that was blocked by former India keeper Adrian.
Bhopal also forced two penalty corners in the opening quarter but failed to score off these as Mumbai slowly came into their own and earned a short corner of their own, also to no avail.
The second quarter was dominated by the home team who stitched moves on the right but some shoddy display inside the striking circle prevented them from going ahead.
Midway through this quarter, Mumbai took a 1-0 lead off a swift counter attack. Joga Singh essayed the ball into the striking circle in the path of Troy Sutherland. The Australian, though fouled by a defender, managed to maintain balance and essay a stiff drive to beat Bhopal custodian Baljeet Singh.
At the end of the halfway stage of the match, Bhopal, for whom Pakistan's most capped player and four-time World Cupper and two-time Olympian Waseem Ahmad turned in an inspired display in the half line right through the encounter, trailed their rivals by the solitary goal.
Mumbai were lucky not to concede the equaliser in the tenth minute of the second half when Sameer Dad's deflection was saved by Adrian.
Three minutes later Badshah's custodian brought off an equally good save from a reverse hit by Devender Walmiki, who combined well with Joga Singh and Sutherland for his team, from the top of the striking circle.
The fourth quarter saw a few goalmouth skirmishes, with Bhopal custodian Baljeet Singh foiling Joga and Sutherland in succession in a melee and at the other end the home team's goal survived anxious moments because of some poor finishing by the Badshahs.
The Bhopal franchise earned their sixth and last penalty corner just before the final hooter, but failed to find the equaliser.
The Marines now take on Comets in their third match on March 4 while the Badshahs travel to Bangalore to take on the Karnataka Lions on March 5.