It was no more than the home side deserved for Hearts started off as strong favourites after beating Rangers in their opening league game.
The visitors' strength in depth was emphasised by Jim Jefferies' decision to leave out midfielder Lee Makel in favour of Steve Fulton while former United favourite Steve Pressley was a substitute.
But United's hard work looked like it might all be in vain when Steve Thompson was shown the red card by the referee, Stuart Dougal, for an innocuous-looking tackle on Gary Locke late in the game.
In the last minute Fulton sent a superb ball through to Neil McCann and the winger saw his fierce net-bound effort pushed away by Dykstra.
And when Fulton returned the loose ball into the danger zone, the former Queen's Park Rangers keeper brought off another fabulous save from David Weir's close range header.
Ally McCoist appeared for the last three minutes at McDiarmid Park, but there was no sign of a goal from any source as St Johnstone and Kilmarnock ground out a draw.
The former Rangers and Scotland international had no complaints about Bobby Williamson's decision. "I know I only got a few minutes, but to be fair he had seen me in training all last week," joked McCoist, who is still searching for match fitness.
Williamson, who retained the team who defeated Dundee United 2-0 on the opening day of the season, was content with a point. He said: "We were away in Europe in midweek so I thought the players handled it well and I've got to be happy."
Kilmarnock created the better chances of a contest that was spirited but lacked quality, the best opportunity falling to Ian Durrant in the closing stages who mis-hit a shot badly when well-placed.
The Saints manager, Paul Sturrock, felt his side were "sluggish" and warned he will look elsewhere if his players continue to produce below- par showings. He said: "It is a long season and you always need to strengthen so there will come a time when we will spend money. I reckon I need three players of a better standard in certain areas of the team - we are certainly looking for another striker.
"We have highly paid professionals here but some of them have let themselves down by not looking sharp enough."
Aside from Rangers' 2-1 win over Motherwell at Ibrox, the Scottish Premier League's only other Saturday fixture saw Dunfermline defeat Dundee 2-0 through goals from Andy Smith and George Shaw.
Last season's First Division title winners Dundee have still to score this season and have now recorded two league defeats as well as a League Cup loss to Alloa.
Jocky Scott, the manager, said: "Bad defending cost us as usual, there was no conviction about our display and we must work harder. The manner we lost the goals upset me. To improve these results we have to learn how to defend well."
The Pars were also surprised in last week's League Cup second round by Livingston, but despite Gavin Johnson's sending-off held on for a vital win with 10 men.Reuse content