It took Brendan Rodgers’ side just nine minutes to take the lead as Jordan Henderson’s pass found Sterling, who fired past Tim Krul for his 11th goal of the season.
Liverpool wasted a host of first-half chances and could have paid the price as Newcastle thought they should have been handed a route back into the match when Dejan Lovren appeared to foul Ayoze Perez in the penalty area, but referee Lee Mason waved the claims away.
The hosts eventually went on to seal all three points thanks to Joe Allen’s smart finish in the 72nd minute before Moussa Sissoko saw red for two yellow cards for the visitors.
The result sees Liverpool reignite their challenge for Champions League qualification before they head to Wembley for next weekend’s FA Cup semi-final against Aston Villa.
After Manchester United’s 4-2 win over rivals Manchester City, Liverpool knew victory would propel them back into the race for Champions League qualification and they started in confident fashion.
They got their reward for their fast start in the ninth minute when the impressive Henderson’s pass found Sterling on the left edge of the penalty area. The England international cut inside and beat two Newcastle defenders before curling a beautiful right foot shot beyond the dive of Tim Krul.
Liverpool went close again minutes later as Lovren found Albert Moreno, who shot from a tight angle but Krul beat the ball away to safety.
The home side were dominant and this time it was Coutinho’s turn to trouble the visitor’s defence. The Brazilian ghosted past Jack Colback and Mike Williamson before cutting the ball across goal, but Sterling could not reach it with the goal gaping.
Newcastle had Krul to thank once again in the 36th minute as he dived full stretch to produce a brilliant one-handed save to keep out Lucas’ free header but despite Liverpool’s dominance John Carver’s men could have been level at the break.
The visitors thought they should have had a penalty when Lovren swung a clumsy leg at Perez. The Croatian defender missed the ball but Mason remained unmoved.
Newcastle were livid but it did not stop them pressing forward and they were only denied an equaliser just before the break by a brilliant diving save from Simon Mignolet as Perez’s header looked destined for the far corner.
Carver’s side started the better of the two sides in the second-half and Mignolet was forced into action again, punching Remy Cabella’s cross clear with Perez waiting to pounce.
Liverpool looked nervy at the back but Sterling tried to get them moving forward again, beating Ryan Taylor but Daryll Janmaat was quickly across to make a vital intervention.
In the 58th minute Sterling was in the thick of the action again and it was a moment he will want to forget. Taylor made a real hash of Henderson's cross and the ball fell to Sterling, who placed his shot wide of the post from six yards.
Liverpool were not made to pay for that miss though as Coutinho’s corner eventually found Emre Can, who dinked the ball to Allen. The Welshman kept his composure to stab the ball past Krul to score his first goal at Anfield.
Newcastle’s night got worse when Sissoko was booked twice in five minutes to hand the club their sixth sending off in as many matches against Liverpool.
Sterling had one final chance to round the scoring off, receiving the ball unmarked 16-yards from goal but he couldn’t keep his shot on target.
Newcastle, who have now suffered five straight league defeats, stay in 13th but Liverpool, who Rodgers believed were out of the race for fourth after defeat at Arsenal, move up into fifth just four points behind Manchester City.
Player Ratings
Liverpool: Mignolet (7), Johnson (6), Can (7), Lovren (5), Moreno (6), Allen (7), Lucas (7), Henderson (8), Ibe (5), Coutinho (8), Sterling (7).
Subs used: Lambert (5), Borini (5).
Newcastle: Krul (7), R.Taylor (5), Janmaat (6), Williamson (5), Colback (6), Anita (5), Abeid (5), Sissoko (4), Cabella (5), Obertan (5), Perez (6).
Subs used: Gouffran (5), Gutierrez (5), Armstong (5).
Man of the Match: Philippe Coutinho