In-form striker Sturridge netted his second of the game in the 105th minute before Henderson sealed the Premier League outfit's progress to round three five minutes later by making it 4-2 with a cool finish.
Those goals came after second-half strikes from Yoann Arquin and Adam Coombes had brought their spirited League One visitors level, following Raheem Sterling's early opener and Sturridge's first before the break.
Brendan Rodgers named a strong team despite the prospect of a Premier League fixture against Manchester United on Sunday, with captain Steven Gerrard and Sturridge both starting, along with the likes of Glen Johnson and Kolo Toure.
Rodgers’ men continued to control proceedings and substitute Daniel Agger - who had replaced the injured Aly Cissokho early on - hit the inside of the post after glancing Gerrard’s set-piece delivery goalwards on 19 minutes.
Sturridge’s movement was causing all sorts of problems for the Notts County backline and the 23-year-old striker was rewarded with his third goal of the season and his ninth in his last eight appearances after 29 minutes with a clinical finish.
However, Kiwomya’s side responded admirably after the interval and their spell of pressure paid dividends around the hour mark when Arquin pulled one back.
And the home side were made to pay for their profligacy when Coombes equalised after good work from Arquin to force extra time.
Nevertheless, Sturridge then found the net against the run of play, as he latched on to substitute Philippe Coutinho's pass before Henderson - who had come on for the injured Joe Allen - burst through from midfield before nutmegging Gary Liddle and side-footing home.
