Chasing 173 to win on what could have been a tricky surface, Kolkata went all guns blazing with Sunil Narine and Lynn getting the visitors off to a flier.
The two put on 52 runs for the opening wicket, with Narine scoring a 10-ball 29 before Shakib accounted for him.
However, Lynn kept on going strongly and completed a deserving half-century before Sidharth Kaul got Sunrisers back in the game.
Kolkata crosses 129 which ensured that they would finish above Rajasthan. Captain Dinesh Karthik was the calming influence for Kolkata despite loss of partners at the other end. Russell and Nitish Rana departed as Kolkata looked to finish the game quickly.
In the end, he stayed unbeaten on 26 as Kolkata registered a comprehensive victory. Kaul was the pick of the bowlers with figures of 2/26 in his 4 overs.
Earlier, Shikhar Dhawan top-scored for the hosts with 50 off 39 balls, while skipper Kane Williamson blazed away to 36 in just 17 as Sunrisers ended at 172/9 in 20 overs.
Young medium pacer Prasidh Krishna's three wickets in the last over was the highlight of Kolkata Knight Riders' fine comeback as at one stage it seemed Hyderabad would post a huge total.
But KKR, who need a win in their crucial last league game to make the play-offs on their own, staged a fightback as SRH managed just 45 runs in the last 7.1 overs after Williamson's dismissal.
The hosts, who have already qualified for the play-offs, were past the 100-run mark in the 11th over.
The 22-year-old Prasidh was the most successful bowler, returning exceptional figures of 4/30 in four overs.
Despite the last collapse, Sunrisers still got to their highest score batting first at home this season.
The Sunrisers were off to a brisk start as Dhawan and Shreevats Goswami (35) added 79 runs in 8.4 overs, an opening record for the home team this season. With his 26-ball 35, Goswami, who has scored a fifty on his IPL debut in the inaugural season, more than made up for Alex Hales' absence.
Dhawan began the SRH innings with a boundary through covers in the first ball of the match and got himself two more off Krishna.
Batting for the first time in this edition of the cash-rich league, Goswami got into the act in style, smashing Andre Russell for 20 runs in the third over.
Two fours and a classy six over extra cover from Goswami and SRH were cruising at 36 for no loss at the end of the third over.
Mystery spinner Sunil Narine bowled an economical first over, conceding just four runs, before Dhawan and Goswami picked up a boundary each off Piyush Chawla.
Dhawan lofted Narine over long-on for a maximum to maintain SRH's healthy run rate, but KKR's last match hero Kuldeep Yadav, after being hit for two boundaries in his first over, castled Goswami with a flighted delivery.
In came the in-form Williamson, and he was off the mark straightaway, with a boundary.
Yadav tried another flighted ball, but Williamson smoked it over long-on for a six, as SRH crossed the 100-run mark in the 11th over.
Williamson then smashed medium pacer Javon Searles for two massive sixes over fine leg, off successive balls, much to the delight of the home crowd at the Rajiv Gandhi International Stadium.
But the cricketer from Barbados had his revenge when he had the prolific Williamsaon caught at deep point two balls later.
Meanwhile, Dhawan was offered a life on 45 when Narine dropped a sitter, but the left-handed India opener could not capitalise and got out for the addition of five runs.
First Published: May 20, 2018, 12:03 AM IST