NFL Most Valuable Player front-runner Jackson tossed a three-yard touchdown pass to Nelson Agholor in the second quarter and showcased his feared running game with a 15-yard rushing touchdown in the third quarter of the Ravens' triumph.
Jackson then delivered the knockout blow early in the fourth quarter, cleverly wrong-footing the Texans defence before hitting Isaiah Likely in the end zone for a score that left Baltimore ahead 24-10 before scampering over for his second touchdown to seal victory.
The top-seeded Ravens will host next weekend's AFC Championship against the winner of Sunday's clash between the Kansas City Chiefs and Buffalo Bills.
"This is just the first play-off game. We're finally in the AFC championship game - we've still got more work to do," said Jackson, who finished with 152 passing yards as well as 100 rushing yards.
The Texans were left reflecting on a disappointing end to a dazzling rookie season for quarterback C.J. Stroud. The 22-year-old from California struggled to get Houston's offence moving in the face of Baltimore's rock-solid defence, finishing with just 175 passing yards.
Houston's points came from a Ka'imi Fairbairn field goal in the first quarter and a 67-yard punt return from Steven Sims in the second quarter.
Justin Tucker's 53-yard field goal kicked Baltimore into an early lead before Fairbairn answered with his own 50-yard effort.
The Ravens were rocked when Sims sliced through the Ravens defence for his punt return touchdown with 4:17 remaining in the second quarter as Houston equalized 10-10 at half-time.
Until Saturday, Baltimore had not been past the divisional round in five play-off appearances since the team won the 2012 NFL season crown.
But Jackson glided 15 yards into the end zone to cap the opening drive of the third quarter for a 17-10 Ravens lead and marched the team 93 yards upfield on a 12-play drive that ended with Likely's touchdown.
Jackson capped a superb individual performance with his second touchdown after another long drive, his eight-yard run making it 31-10 and Tucker added a late 43-yard field goal.
