Stevenson's nasty tackle provoked Walker, who went for his opponent and deliberately clashed heads. Neither player was punished by Willie Collum, the referee.
Hearts maintained their 100% record in the SPFL Championship with a 2-1 win in a match which ignited only towards the end, with all three goals and two red cards in the final 13 minutes. Sam Nicholson and Prince Buaben scored for Hearts, Farid El Alagui pulled one back for Hibs and both Scott Robertson and Osman Sow were sent off.
Hibs, who missed a first-half penalty, felt Walker should have been punished over the late incident, which sparked a melee near a corner flag. Walker retaliated to Stevenson's ugly lunge when Hearts were wasting time in the dying minutes. No force was used when he put his head against Stevenson's but the act itself could land him in trouble.
Vincent Lunny, the SFA compliance officer, inevitably will look at footage of the match and decide whether either player should face a notice of complaint for violent conduct. "I'm sure people will have a look at it," said Michael Nelson, the Hibs defender. "If there was a head used you can't get away with that these days, you get found out sooner or later," said Alan Stubbs, the Hibs manager. "I think the lad put his head on one of our players at the end. It will be interesting to see what happens."
Nelson needed treatment, and wore a bandage around his head, after a flying elbow from Sow cut him near the eye in the first half. A repeat of the incident led to Sow being shown a straight red card with two minutes left. "It probably took 70 minutes too long for it to get punished," said Nelson. "I don't know if it was intentional, only he can tell you that. I couldn't care less if it was or not."
The result condemned Hibs to a third consecutive derby defeat but there was little between the teams. "We didn't look in any trouble and then within a few minutes we found ourselves 2-0 down," said Stubbs. "A defeat feels like we've been robbed."
Hearts head coach Robbie Neilson has delivered wins over Rangers and Hibs, their two strongest title rivals. "It obviously helps the confidence and the belief but it's six points, that's all," he said. "We go to Raith Rovers next week and need to win again. We need to be relentless and just keep winning.
"We created a few chances. Not a lot of clear-cut ones but we did enough to win it. I thought we had the players that, after 70 minutes when the game starts opening up, can go into areas with a bit of quality, and we got that with Sam. We waited 90 minutes for him to do it at Ibrox. We got it after 70 minutes today."