The Hatters were on a high after two wins out of two following promotion from League One last season - both against teams who were in the Premiership last season.
And they were in charge again in this showdown with Leeds - a side that four years ago was playing in the semi-finals of the Champions League.
Luton dominated the first-half, but could not find the goal that their patient build-up play deserved.
While Leeds relied on the long ball up to Michael Ricketts, the home side were content to keep possession and try to play their way through the defence.
And they were good value for a half-time lead and were unfortunate not to grab one, especially when Steve Howard saw a 25th-minute effort hit the post.
Defender Curtis Davies set up the chance as he surprisingly popped up on the Leeds by-line before delivering a dangerous ball into the six-yard area.
Howard slid in with Leeds centre-back Paul Butler and connected with the ball, but although it beat goalkeeper Ian Bennett the woodwork came to the visitors' rescue.
Luton maintained their stylish approach with Kevin Nicholls pulling the strings at the heart of midfield and Dean Morgan providing danger down the right.
Steve Howard's aerial strength also disrupted the Leeds defence, but it was midfielder Ahmet Brkovic who had the next pop at goal.
The Croatian had scored in both the previous two games and appeared to believe he had turned into Marco van Basten as he unleashed a volley from wide on the right which was reminiscent of the Dutchman's amazing strike in the 1988 European Championships Final.
And Brkovic's effort was almost as good as it flew just over the bar with Bennett beaten.
Leeds were disappointing in the first 45 minutes as they lacked any cohesion and truggled to string together more than two or three passes.
However, they could have grabbed a goal on the stroke of half-time when Nicholls made his first poor pass of the game and gifted possession to Shaun Derry.
Leeds sprung forward and Ricketts was sent clear 16 yards from goal, but typical of his entire first-half display he produced a lazy-looking finish which slid wide of the post.
The second-half was less entertaining than the first as Leeds tightened up in defence, apparently content to return to Yorkshire with a point.
As a result, Luton struggled to get in behind them as they had done in the opening period, with Howard less of an influence on the game.
However, they would have claimed the win but for the superb intervention of Bennett from a Nicholls' 73rd-minute free-kick.
The midfielder's floated effort round the wall from 20 yards was destined for the top corner before the Leeds goalkeeper tipped round the post to keep the scores level.
And despite a late onslaught from the home side, with the giant Enoch Showunmi thrown on to cause chaos up front, that was the way it stayed.