Lawrence put the home side ahead with a penalty after Matt Connolly fouled Dave Kitson in the box and was then dismissed after handling the ball in the area and giving Tommy Smith the chance to earn a point for the league leaders from the penalty spot.
Steve Cotterill made two changes to the side that lost at Derby, with Kanu partnering Kitson up front and Greg Halford starting at the expense of Joel Ward. Neil Warnock made only one change for the trip to Fratton Park, with Clint Hill replacing the suspended Bradley Orr.
In the opening exchanges, both sides were very evenly matched and Michael Brown had the first shot of the game but fired wide of the post from 25 yards.
This sparked QPR into action and they responded immediately through former Pompey midfielder Shaun Derry, who saw his shot saved by Jamie Ashdown. Soon after, dangerman Adel Taarabt crafted an opening for Alejandro Faurlin but his shot went high and wide of the target.
Kanu provided a strong presence up front for Pompey and almost created the first goal of the game but his cross just evaded the lunging Lawrence, who couldn't find the vital touch to put the ball into the net. The Nigerian then had a chance of his own but his deflected shot was easily taken by Paddy Kenny in the Rangers goal.
Pompey had the best chance of the opening half when John Utaka raced clear and cut inside to fire a fierce shot that cannoned back off the crossbar.
After the interval Pompey pressed with Brown seeing his shot fly narrowly over the bar. Rangers once again came back into the game and Rob Hulse had a great chance to open the scoring but his header was brilliantly saved by Ashdown after a great cross from Smith.
The game sparked into life on 70 minutes when Connolly was given his marching orders after bringing down Kitson in the box. Lawrence stepped up to take the penalty but Kenny saved his effort - only for the referee to order the spot-kick to be retaken. Lawrence made no mistake at the second time of asking and smashed the ball into the back of the net to give Pompey the lead.
QPR pushed hard for an equaliser and were given a lifeline in the 90th minute when Lawrence was adjudged to have handled a Smith cross. Lawrence was given his second booking before Smith stepped up and placed the ball beyond Ashdown to keep Rangers top of the table.