World number one Selby beat China's Tian - who built the only century of the last-four stage - 4-2 while Dott whitewashed Lawler 4-0.
In the last eight, former world champion Dott won an entertaining quarter-final 4-3 against Ben Woollaston who compiled two century breaks.
Mark Selby 4-2 Tian Pengfei
Graeme Dott 4-0 Rod Lawler
Graeme Dott 4-3 Ben Woollaston
Tian Pengfei 4-2 Martin Gould
Mark Selby 4-0 Thanawat Tirapongpaiboon
Rod Lawler 4-3 Kurt Maflin