Callum Paterson headed home the only goal in the 71st minute to give diehard Hearts supporter Locke his first victory in the derby as manager.
The victory was all the more impressive after forward Stevenson, one of only two outfield players over the age of 21 for the hosts, reluctantly limped off after 13 minutes after failing to recover from a 50/50 challenge with Scott Robertson.
The three points were their first inroads into the 15-point penalty handed down to them after they were plunged into administration and Locke, whose side were beaten in last week's Scottish Premiership curtain-raiser at St Johnstone, said: "It's a huge, huge win.
"It did not matter who we were playing, getting the first win and putting a wee bit of pressure on the teams above us was huge and it helps against your biggest rivals as well.
"The fans have been through a lot over the summer and hopefully that will be a result that keeps them happy tonight.
"It gives everyone at the club a lift, I was not too disappointed when we lost last week and I'm not going to get too carried away today.
"The sooner you get a win with the situation we're in, the better. We've done that and now we have something to build on.
"It certainly was not a classic but you saw two teams that were competitive and one wee bit of quality has won us the game."
But Locke admits he is fearing the worst over Stevenson, with early signs suggesting he has damaged medial ligaments in his knee.
He added: "I will probably find out more on Monday, it looks a bad one, maybe his medial ligaments.
"It looks like I'm going to lose him for a number of weeks which is a huge blow because everybody knows we don't have the biggest of squads and he is a valuable player.
"He's getting a scan on Monday so we'll find out more then. It's not going to be great news whatever happens but I'm hoping he's not going to be out too long."
Embattled Hibs manager Pat Fenlon, meanwhile, admits he is expecting questions to be asked over his stewardship following a disappointing start to the season.
The Leith club lost 9-0 on aggregate to Swedish side Malmo in the Europa League and have been defeated in their two opening league matches against Motherwell and Hearts.
Fenlon said: "I've got no problem with people looking at my position, no problem at all. I'm the manager of the club and I will continue to do that.
"We've lost two games 1-0 in the league and Europe was really disappointing. In both league games there was very little in them and I don't think we're too far away from getting a result. I'm very happy with the squad we have.
"We need one result, footballers live confidence-wise and a result on the board helps, it breeds confidence.
"There has been very little in the games we played and with a break of the ball, we could have got a result."