Melbourne skipper Cameron Smith overcame a serious ankle injury to play but his presence wasn't enough to stop the Canterbury onslaught.
Eastwood set the tone early with a massive hit that flattened Storm winger Sisa Waqa.
Two minutes later he scored after Michael Ennis put up a towering bomb that Lafai batted back to the backrower.
Bulldogs halfback Trent Hodkinson found a gaping hole in the Storm defence and the scoreline was then out to 18-0 after just 18 minutes when Lafai intercepted a Ben Roberts pass and raced 55m to the line.
The visitors weren't done and Lafai added his second after some handy lead-up work by Josh Jackson and Klemmer for the impressive half-time margin.
The Storm tried to force their way back into the match but too often errors ruined any attacking opportunities.
Waqa finally broke the drought in the 45th minute when he leapt high for a pin-point kick by Storm halfback Cooper Cronk.
Two moments then proved telling of the Storm's day.
Waqa looked to have scored after a break by fellow winger Marika Koroibete only for the video referee to rule an earlier knock-on.
Soon after Waqa made a break and popped a ball for Mahe Fonua, but prop Graham somehow ran down the speedsters and managed to stop a certain four-pointer.
Still trailing by 20 points, the Storm ran out of time and ideas, Eastwood snatching an intercept to race 50m before off-loading to Lafai for his third of the day.
Week 2 finals
Fri 9:55pm - Roosters Vs Cowboys
Sat 9:45pm - Manly Vs Bulldogs
- AAP
