It seemed like there would be an anxious end when Dejan Damjanovic pulled one back for the visitors but Townsend then scored and Daniel Sturridge netted from the penalty spot in stoppage time.
Hodgson pulled off a surprise by naming Townsend in the starting lineup for his first cap, capping a whirlwind year for the Tottenham winger.
Four months ago, Townsend withdrew from the squad for the European under-21s championship before receiving a one-month ban and a fine of 18,000 pounds ($27,000) for breaching betting regulations.
But a strong start to the season with Tottenham saw Townsend force his way into the senior international fold.
From the start Friday, the 22-year-old Townsend used his pace down the right flank to trouble the visiting defense.
"It can't be easy for a young player making his debut," Hodgson said. "He played with calmness and composure."
Although Montenegro began to crowd out Townsend he managed to pick out Frank Lampard, who set up Steven Gerrard as the pressure built from Hodgson's side.
England was facing a goalkeeper who, like Townsend, recently served a ban for breaching integrity rules. Vukasin Poleksic's two-year suspension was for failing to report that match-fixers approached him before a Champions League match.
Poleksic didn't have a save to make until the 22nd minute, blocking Welbeck from a tight angle, and Joe Hart in the England goal was similarly quiet.
England's best opening was squandered just before halftime when Townsend had a low shot spilled and Rooney bundled the follow-up into the sidenetting.
"It was a tough game at halftime, you saw how difficult to break down they were, and well organized," Hodgson said.
But Townsend ensured England made the perfect start to the second half after charging down the right and whipping in a cross that was half-cleared. Welbeck's resulting shot was parried but Rooney managed to scuff the rebound into the net in the 49th minute.
It was the Manchester United striker's sixth goal in five qualifiers.
England's Kyle Walker was then booked for a shirt-tug and the right back is now suspended for Tuesday's finale.
But luck turned back in England's favor in the 62nd.
A backheel from Sturridge released Welbeck on the left flank, and his cross was inexplicably turned into the net by Boskovic when under no pressure.
England had chances to extend its lead through Sturridge and Welbeck, and seemed to be cruising when Montenegro pulled one back to ensure there would be an anxious end. Against the run of play, Dejan Damjanovic turned Fatos Beqiraj's shot beyond Hart in the 72nd.
But the two-goal lead was restored six minutes later. Townsend picked up ball near halfway line and ran through the defense before sending a swerving shot in off the right hand post.
The three points were no longer in doubt, and the gloss was put on the win by Sturridge's penalty after the Liverpool striker was brought down.
In Kharkiv, the only goal was scored by Andriy Yarmolenko in the 64th minute, ending Poland's qualification hopes.
The Ukraine winger curved a left-footed shot from the center of the box after being left alone by the Polish defense who instead risked intercepting Yevhen Konopolyanka's cross.
