Stubbs and Porel's explosive batting set a strong foundation.
Ishant Sharma's 3-34 in the powerplay left Lucknow struggling at 44-4.
Pooran's 61 off 27 balls revived Lucknow's innings.
Abishek Porel and Shai Hope built a crucial 92-run partnership.
Stubbs smashed four sixes and three fours in his unbeaten 57.
Mukesh Kumar and Rasikh Salam conceded only nine runs in the final overs.
Arshad Khan's explosive 58 not out off 25 balls supported Lucknow's chase.