The Three Lions opened their qualification campaign with a 5-0 victory over Czech Republic on Friday, but they had to come from behind to pick up another three points in Podgorica.
As for the hosts, star forward Stevan Jovetic was unavailable through injury, but Atletico Madrid centre-back Stefan Savic did overcome a hamstring issue to start. Lazio's Adam Marusic and Levante's Nikola Vukcevic, meanwhile, both made the XI.
It did not take long for England to gain control of the possession in the Group A clash, with Sterling and Hudson-Odoi seeing plenty of the ball in wide positions, while Rice and Barkley were in control of the midfield.
England again came close in the 12th minute when Sterling danced into the home side's box before delivering a cross onto the boot of Dele Alli, but Savic was on hand to make an excellent block.
Montenegro hardly ventured out of their own half in the first 16 minutes, but they incredibly took the lead in the 17th minute when Vesovic managed to work his way into the England box before curling a stunning effort past the reach of Jordan Pickford.
Savic made a wonderful defensive header to clear a cross from Hudson-Odoi in the period that followed as England looked for a leveller, but it was not quite happening for Gareth Southgate's side.
The Three Lions continued to press, though, and equalised on the half-hour mark when Keane jumped above Savic to head a deep Barkley free kick into the bottom corner of the Montenegro net.
Pickford had to keep out a powerful strike from Stefan Mugosa in the 34th minute with Montenegro still threatening, but England completed the turnaround in the 39th minute.
It initially appeared that Hudson-Odoi's strike had flown straight into the back of the net, but Barkley got the vital touch as the Chelsea midfielder netted just his third international goal.
Montenegro were still carrying a threat in attack as the first period approached its final moments, but the whistle blew with England leading courtesy of goals from Keane and Barkley.
Neither manager looked to their bench at the interval, which was not too much of a surprise as both Ljubisa Tumbakovic and Southgate would have been fairly pleased with what they saw in the first period.
England had a golden chance to score a third in the 49th minute when a deep cross from Hudson-Odoi found Sterling, but the Manchester City attacker fired over the crossbar at the far post.
Hudson-Odoi then saw his low strike well saved by Petkovic moments later as the Three Lions looked to take the match away from Montenegro in the early stages of the second half.
The hosts were still carrying a threat, however, and Fatos Beqiraj had a brilliant opportunity to level the scores in the 54th minute, only to turn wide of the post from close range.
England took a huge step towards securing all three points just before the hour, though, with Barkley sweeping a deflected Sterling cross into the back of the net to send the away side 3-1 ahead.
The 2018 World Cup semi-finalists were not finished, however, and made it 4-1 in the 71st minute when Kane tapped a low cross from Sterling into the bottom corner from close range.
There were plenty of opportunities for the visitors to score more goals on the break, with Montenegro committing players forward in a bid to grab their second of the evening.
England's fifth ultimately arrived in the 81st minute when Sterling collected a through pass from Jordan Henderson before slotting into the back of the net for his fourth goal in two games.
England's next fixture is against an in-form Netherlands in the semi-finals of the UEFA Nations League on June 6, while Montenegro will play their third Euro 2020 qualifier against Kosovo on June 7.
MONTENEGRO (4-4-2): Petkovic; Tomasevic, Simic (Jovovic 74'), Savic, Stojkovic; Vesovic (Boljevic 70'), Vukcevic, Ivanic, Marusic; Mugosa, Beqiraj (Jankovic 61')
ENGLAND (4-3-3): Pickford; Walker, Maguire, Keane, Rose; Barkley (Ward-Prowse 82'), Rice, Alli (Henderson 64'); Sterling, Kane (Wilson 83'), Hudson-Odoi