An action-packed first half saw Abraham and fellow academy product Mason Mount twice put the visitors ahead but first Todd Cantwell and then Teemu Pukki levelled.
The Europa League winners took the lead for the third time through Abraham's well-taken second after the interval and held on to claim all three points at Carrow Road.
Man of the match
Coming into the match Lampard called for his strikers to be more "clinical" in front of goal and Abraham certainly took that on board, netting with the first chance of the match.
The 21-year-old's movement and pace caused the hosts problems all afternoon and after just staying onside, confirmed after a VAR check, he beat two Canaries defenders before dispatching the winner.
"Two wonderful finishes, which looks like it will get the manager his first win and a big three points." - Chris Sutton
View from the dugout
Farke unhappy with allotted stoppage time
The Norwich boss insists the officials were not to blame for the defeat but does question how more time was not added on at the end of the second half when they were chasing an equaliser.
Lampard relieved to earn first Chelsea win
Despite securing his first three points as manager, Lampard still calls for his forwards to be more clinical in front of goal and bemoans the two they gave away.
View from the dressing room
Abraham - Dream come true to score first Chelsea goals
The two-goal hero talks about ending his wait for a first in Chelsea blue and reflects on a difficult afternoon against the newly-promoted outfit.
Cole: Lampard will flourish playing Chelsea youth
Former Chelsea midfielder Joe Cole believes Abraham and Mount deserve their place in the team and it will benefit Lampard in the long run as both were on target at Carrow Road.
Tweet of the game
Lampard said he would give youth a chance and he certainly has. That faith has been rewarded as all four of Chelsea's league goals this season have been scored by academy products.
21 - This is the first time two English players aged 21 or under have scored in a Premier League match for @ChelseaFC since 22nd August 1992, when Eddie Newton and Graham Stuart scored against Sheffield Wednesday. Throwback. #NORCHE pic.twitter.com/fUQ9T5ksUs— OptaJoe (@OptaJoe) August 24, 2019
Picture of the game
That's what a first win means to Lampard.
There were several decisions the panel covered with former Premier League referee Peter Walton post match, including this potential Chelsea penalty.
Chris Sutton insists there was contact on Cesar Azpilicueta but Walton was adamant there was not enough contact for VAR to get involved.
• Chelsea boss Frank Lampard has lost none of his three managerial meetings with Norwich (W2 D1), winning both of his visits to Carrow Road (also 4-3 with Derby in December 2018) – Mason Mount has been on the scoresheet in both such wins.
• Norwich have scored at least twice in 16 of their last 17 home league games, scoring a total of 46 goals in this period. However, this was their first home league defeat of 2019 (P12 W8 D3 L1).
• Both Norwich and Chelsea had scored after just five minutes and 32 seconds, the earliest time taken for both teams to find the net in a Premier League fixture since November 2017, when Crystal Palace v Everton was at 1-1 after 5:25.
• Chelsea striker Tammy Abraham has scored 28 league goals (including play-offs) since the start of last season, the most of any English player in the top two tiers of English football in that time.
• Aged 21 years and 326 days old, Tammy Abraham is the third youngest player to score a brace in the Premier League for Chelsea, after Mark Nicholls in January 1998 against Coventry (20y 225d) and Eddie Newton in December 1992 against Tottenham (20y 358d).
• Norwich forward Teemu Pukki (five goals) is the 10th player to score in each of his first three Premier League appearances, while only Pavel Pogrebnyak also scored as many as five in his first three in the competition.
• Norwich’s Todd Cantwell (one goal, two assists) has already been directly involved in as many Premier League goals in three games as he was in 24 Championship appearances last season.
• Since the start of last season, Norwich's league matches have seen a total of 164 goals scored (99 for, 65 against), more than any other side in the top four tiers of English football in this time (excluding play-offs).
Crawley (A) - Tuesday 27 August, 7.45pm (League Cup, second round)
West Ham (A) - Saturday 31 August, 3pm
Man City (H) - Saturday 14 September, 5.30pm
Sheffield United (H) - Saturday 31 August, 3pm
Wolves (A) - Saturday 14 September, 3pm
Liverpool (H) - Sunday 22 September, 4.30pm
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