David Warner (L) with teammate during the match in Mumbai on Sunday. Courtesy IPL
The left-right opening pair of Warner (61) and Shaw (51) put on 93 runs to lay the foundation for Delhi's 215 for five — the highest total of the season so far — in the first match of the day in Mumbai.
Left-arm wrist spinner Kuldeep Yadav then returned figures of 4-35 to help bowl out Kolkata for 171 in 19.4 overs in the IPL Twenty20 tournament.
Shaw raised his second successive half-century in 27 balls to get Delhi off to a flier but soon fell to mystery spinner Varun Chakaravarthy.
Warner, the swashbuckling Australian batter who was picked by Delhi for $826,000 in the February auction, kept up the charge and reached his fifty with a six off Andre Russell.
Warner said he is "absolutely loving" his time with Delhi Capitals, who are coached by Australian great Ricky Ponting and looking for their maiden IPL title. "He is a like a father and a big kid to be honest," Warner said of coach Ponting. "Obviously he has got lot of respect, great knowledge about the game. He is a great coach. Everyone's happy to be underneath him."
Warner finally fell to pace bowler Umesh Yadav but Axar Patel (22) and Shardul Thakur (29) steered the team to the big total with an unbeaten stand of 49 off 20 balls.
Skipper Rishabh Pant also contributed with a quickfire 27.
In reply, Kolkata lost early wickets with pace bowler Khaleel Ahmed sending back openers Venkatesh Iyer, who made 18 off eight balls, and Ajinkya Rahane, who struggled to get eight, in his first two overs.
Skipper Shreyas Iyer, who smashed 54, and Nitish Rana, who hit 30, attempted to rebuild with a partnership of 69 but the Delhi bowlers hit back and rattled the opposition batting.
Kuldeep got Shreyas stumped after the captain's 33-ball blitz and Khaleel sent back Sam Billings out for 15.
Kuldeep in his fourth over struck thrice including two on successive deliveries and finished with a superb diving catch off his own bowling to send back Umesh for nought.
Thakur wrapped up the Kolkata innings as he got Russell out for 24 and Rasikh Salam for seven.
Punjab Kings shelled out $2.23 million on the all-rounder but they are eighth in the 10-team table and barring a miracle will not qualify for the knock-out phase.
Bowling brilliantly and in the channel, Shami sent back Lucknow skipper and his India teammate KL Rahul for a golden duck and then claimed two more wickets in quick succession for figures of 3-0-10-3 in his first spell.
Lucknow Super Giants (LSG) rode on blazing half-centuries by Evin Lewis (55 off 23 deliveries) and Quinton de Kock (61 off 45) to beat Chennai Super Kings (CSK) by six wickets and register their first victory in the IPL 2022 at the Brabourne Stadium.
Qualifier 1 and Eliminator will be held at the Eden Gardens in Kolkata on May 24 and 26 while Eliminator 2 will be in Ahmedabad on May 27 and the final of the cash-rich league will be held at the Narendra Modi Stadium on May 29.
Eighteen Pakistan players and 15 support staff are due to travel to India. Earlier, the PCB had expressed its disappointment with the ICC over the delays.
UAE Equestrian and Racing Federation announced that its four-strong dressage team has passed the vet check and will go on to compete on Tuesday, in the team competition and individual qualification.
Lock Thibaud Flament studied at Loughborough University in England, full-back Melvyn Jaminet had never played a Top 14 game and winger Gabin Villiere was a second-team scrum-half in the French fifth-tier before bursting onto the international scene.
Batting first India reached 116-7 in their 20 overs with Smriti Mandhana (46) and Jemimah Rodrigues (42) putting on 73 for the second wicket. Sri Lanka's chase started badly when they were reduced to 14-3 in the fifth over by a devastating spell from right-arm seamer Titas Sadhu.