Yahya Al-Shehri, Osama Hawsawi, Taisir Al-Jassim, Naif Hazazi and Fahad Al-Muwallad also got on the scoresheet while the home side's woes were compounded when Adelino De Oliviera was sent off in the 88th minute for picking up a second booking.
Saudi Arabia's emphatic win extended their lead at the top of the Group A standings to six points and left them in a commanding position to advance to the third qualifying round.
The eight group winners and four best runners-up will all progress to the next phase and also book a spot at the 2019 Asian Cup.
Unbeaten in six matches, the Green Falcons currently have 16 points with two games to go. Only the United Arab Emirates, who have 10 points but a game in hand, can catch them at the top.
Al-Sahwali has been the driving force behind his team's success and is the leading scorer in the tournament with 12 goals from five matches.
"These are three important points and it was important to win here," Al-Sahwali said in a televised interview.
"It is not important who scored the goals but the win is the important thing. I hope this result will help us to keep our position till the end"
The 28-year-old also scored three goals against the Timorese in their previous meeting in Jeddah in September and showed no mercy against the same opponents on Tuesday.
East Timor, winless in their seven qualifiers, were without seven naturalised Brazilians following complaints about their eligibility after they earlier helped their adopted country draw with Malaysia and Palestine.
They did well to hold Saudi Arabia scoreless for almost half an hour before Al-Sahwali opened the scoring in the 29th minute, with the first of two penalties he converted.
He scored again just before halftime as the visitors went to the break leading 4-0 then added a second half hat-trick as the Timorese faded badly in the oppressive heat, giving up four goals in the last 10 minutes.
"It may seem to be an easy win, but it is not that easy after all players exerted their maximum effort," Saudi Arabia's Dutch coach Bert van Marwijk said, speaking through a translator.
(Reporting by Julian Linden and Osama Khairy; Editing by John O'Brien)
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