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 in the 13th minute 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.
"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.
"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 isfearing 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."