Robinson, who signed a new two-year contract last Tuesday, moved up to score at the far post with a header from substitute Riccardo Scimeca's cross from the right to notch his first ever goal for Albion.
Aston Villa had appeared to be heading for victory thanks to Darius Vassell's first-half goal. He looked to be back to his best form and will be looking for a recall to the England squad.
But it was a match marred by the fact that both teams finished with ten men after Villa's Liam Ridgewell and the Baggies' Jonathan Greening were both sent off in the 61st minute for alleged head-butting following a seemingly harmless incident.
In the circumstances Villa were deeply indebted to Vassell's first-half goal as they collected only their second point from four local derby games.
Vassell has struggled following a spate of injuries but he led Albion a merry dance with his pace and goalscoring attempts which were eventually rewarded with his 27th minute strike.
The goal was a particular milestone for Vassell as it was his first Premiership goal since the opening match of the season.
Albion last won at Villa Park in 1979 and there was rarely any indication of them breaking this unfortunate run in their desperate bid to improve their Premiership survival hopes.
Albion's newly acquired confidence, however, was evident in the early stages as they survived some early Villa pressure without too much difficulty but they were unable to push forward with any real conviction.
The eager play of Kieran Richardson and Zoltan Gera was a key reason as they competed for midfield control against Lee Hendrie and Stephen Davis.
Villa's attacking threat was more evident but Russell Hoult was in good form as he bravely blocked an effort from Vassell and then saved a long-range effort from Hendrie.
He made another brilliant save to flick over a cross from Jlloyd Samuel but from Nobby Solano's corner Villa took the lead.
Ridgewell, deputising for Villa's injured skipper Olof Mellberg, powerfully headed goalwards where Hoult parried the ball upwards and to his right for Vassell to head home from close range in the 27th minute.
It was not until the last few minutes of the first half that Albion finally managed to test Thomas Sorensen with a shot from Gera and a close-range header by Kevin Campbell which the Villa keeper held at the second attempt.
Moments later Sorensen had to make another save from Campbell and five minutes into the second half Martin Laursen cleared off the line as Geoff Horsfield closed in to apply the finishing touch.
Following the sending off of both Ridgewell and Greening the game became a little frantic with Vassell being denied a second goal by a great save from Hoult.
There was an equally fine save by Sorensen to deny Robinson equalising after he had been put clear by Campbell.
But Sorensen was beaten in the last few seconds when the former Watford defender Robinson headed a goal which could inspire Albion's late survival bid.