With a gigantic target to eclipse, RCB needed a rollicking start but the visitors' chase never got going as they kept on losing wickets to be bundled out for 113 in 19.5 overs.
While Warner celebrated with glee on scoring his 4th IPL century, Jonny Bairstow smashed his maiden IPL ton in his first season in the cash-rich league.
The SRH opener went absolutely berserk as he hammered his maiden IPL ton off 52 balls against Royal Challengers Bangalore in Hyderabad.
At 16 years and 157 days, the Bengal spinner snatched this record from Afghanistan spinner Mujeeb ur Rahman.
Opening for the first time in 28 matches Bairstow broke the back of a 161-run target, which owed much to Rashid's miserly return of 1-15.
Bairstow scored 110 off 186 balls, with nine fours and a six, in his first game since twisting his ankle while playing football almost a month ago during the ODI series against the Sri Lankans.
Ben Foakes will continue with the gloves in the 2nd Test as there seems to be no space for Jonny Bairstow after the former notched his maiden ton on his debut.
The former Sri Lanka skipper is retiring from all forms of cricket in Galle after this first test of three.
Bairstow fractured a bone in the middle finger of his left-hand midway through the third Test in Nottingham, which India won to reduce the deficit in the five-match series to 2-1.
Bairstow injured his finger while keeping the wickets in India's second innings and after that Jos Buttler kept the wickets.
Jos Buttler took over the wicket-keeping responsibilities after Bairstow suffered the injury.
His captain Joe Root had said after the second Test win at Lord's that a 5-0 result would be a dream.
Woakes struck his first Test century to guide England to 357/6 and a commanding 250-run lead over top-ranked India.
Bairstow, who is Rashid's team-mate in Yorkshire, refused to be drawn into the controversy but said the leg-spinner must be excited to have got the England call-up.
After the T20 series defeat and the drubbing in the ODI opener, England registered convincing wins in the next two matches to claim the rubber 2-1.
With the mammoth total today, England surpassed their own highest ODI total of 444/3 that they scored against Pakistan at the same venue on 30 Aug 2016.
Jonny Bairstow and Mark Wood helped mask the deficiencies of an England batting lineup which earlier had been exposed by Tim Southee, who took 5-60.
Bairstow posted his century with eight fours and six sixes and reached 104 from 60 balls as he helped the visitors clinch a nail-biting series 3-2.
Limping and often grimacing in pain, the 34-year old Taylor hit the 19th ODI century of his career, surpassing his highest score of 131 and steered New Zealand to 339/5 with three balls to spare.
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