Ipswich were decent value for their point, which lifted them out of the relegation zone.
Their wait for a first win since returning to the Premier League goes on, although manager Kieran McKenna will take positives from this latest display.
Delap's two goals were both well taken but quite different in execution.
His first was a predatory first-time strike from inside the penalty area and his second was all of his own making, reminiscent of his first Premier League goal for Ipswich in the 1-1 draw against Fulham on 31 August.
The 21-year-old perhaps should have had a hat-trick, but Martinez denied him when he was sent through for a one-on-one in the first period.
Kalvin Phillips had a hand in Ipswich's opener, winning a turnover deep in the Villa half before feeding Clarke to set up Delap.
England international Phillips also tested Martinez with a stinging drive from outside the penalty area.
Of concern to McKenna will be the defensive lapses that led to two soft goals at the other end.
Ipswich's next four league fixtures are against teams currently outside the top 10, so hopes of a first league win of the campaign arriving soon will be high - especially if Delap can continue this fine start to his career in Suffolk.