The Tigers needed all five games to win the American League Division Series and Verlander was the winning pitcher in two of the three Detroit victories.
Detroit will now meet either the New York Yankees or Baltimore for the AL pennant. New York and the Orioles will also meet in a Game 5 on Friday.
Verlander, the author of two no-hit games in his career, gave up three hits in seven innings while capturing the series opener against the A's.
This time he went the distance for the first time in 10 career post-season starts, allowing one walk and striking out 11. Oakland advanced only two runners as far as second base.
Verlander again got the best of Jarrod Parker, who faced him in Game 1 of the series with similar results.
The Tigers broke things open in the seventh, scoring four times while sending 10 men to the plate and leaving the bases loaded.
Jackson also had an RBI in the seventh and scored the third run of the inning on a single by Prince Fielder.
This will be Detroit's second consecutive appearance in the ALCS. The Tigers fell to the Texas Rangers in six games last year.
Oakland saw an unexpectedly successful season come to an end. The A's came from four games behind with six to play to grab the American League West pennant away from Texas and then staged a dramatic comeback in Game 4 of this series to keep their campaign alive for one more day.