The Nizams remain unbeaten in the competition while JFC are yet to taste victory.
Valskis scored in the 30th and 66th minute while Roy Krishna pulled one back for ATKMB in the 80th minute.
Chennaiyin FC went through to the final 6-5 on aggregate, thanks to their 4-1 victory at home in the first leg.
Mumbai City FC ended their seven-game winless run in the Indian Super League (ISL) with win over Chennaiyin FC
On a night of missed opportunities, the two-time champions rode on goals from Rafael Crivellaro and Nerijus Valskis in the 57th and 59th minutes respectively to pocket three points, which takes it to sixth in the points table with 15 points.
ATK's David Williams scored the all-important goal in the 48th minute to seal the win on a day when Chennaiyin FC did everything but score.
Here is a round-up of results from the ISL and I-League matches played on Monday
After three losses on the trot, laggards SCEB finally opened their account
India international Anirudh Thapa scored in the first minute to set up Chennaiyin FC's 2-1 win over Jamshedpur FC in an Indian Super League match, in Vasco, on Tuesday.
Bengaluru took just three minutes to register their first shot on target. Kristian Opseth's free-kick nearly curled into the bottom corner, only to be kept out by a diving TP Rehenesh.
This result meant a win for ATK Mohun Bagan against Hyderabad FC on Monday would ensure them of the League Winners Shield and a maiden AFC Champions League spot.
Two-time champion Chennaiyin FC opened its account in ISL-6 with a goalless draw against Mumbai City FC in its first home game of the season at the Nehru stadium, in Chennai, on Sunday.
Brandon Fernandes had a chance to put his side ahead in the game early on when he was set up by Jorge Ortiz on the left. The midfielder got the ball at the edge of the box and curled at the far post but only to see his attempt miss the top corner.
Mumbai unleashed wave after wave of attacks, but to no avail. Mourtada Fall blazed one over in the 38th minute, while a couple of minutes later, Ogbeche headed wide from close range. The Jamshedpur defence held firm as both teams went into the break on level terms.
It was Chennaiyin FC's first win in 289 days, bringing a lot of relief for Gregory, who two weeks ago was contemplating an exit.
Goian's 83rd-minute strike was enough for Chennaiyin to win the contest 1-0 and complete the ISL play-off lineup.
ATK may have qualified for the play-offs, but the loss came as a big blow to their AFC Champions League qualifying aspirations with FC Goa taking a three-point lead at the top with only a match left for the league stage to conclude.
Chennaiyin FC and Odisha FC shared the spoils after a thrilling 2-2 draw in the Hero Indian Super League, at the Jawaharlal Nehru stadium, in Chennai, on Thursday.
A rampaging ATK claimed an unprecedented third Indian Super League title triumph with a 3-1 victory over arch-rival Chennaiyin FC in a summit showdown that was played behind closed doors in Margao on Saturday. Javier Hernandez (10th minute) and Edu Garcia (48th) put ATK in the driving seat but Nerijus Valskis (69th) reduced their advantage to set up a tense end to the contest. Hernandez scored another in injury time (90+4th) to confirm a record third title.
Bengaluru now have two draws in a row and their first clean sheet but languish at second-last with just six points.
Goals from Matti Steinmann (6th) and Anthony Pilkington (68th) secured the victory for SCEB
FC Goa returned the favour just four minutes later when Seriton Fernandes and Alberto Noguera played a quick one-two, before sending the former free on the right flank.
ATK now have 33 points as they remained firm in contention for the top-spot.
After constant pressure, Bengaluru were finally rewarded with the equaliser in the 82nd minute when Paartalu nodded in Cleiton's in-swinging corner.
All the results from the I-League and ISL matches played on Sunday
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The 2021 men's and women's U-17 European Championships have been cancelled due to the impact of the COVID-19 pandemic, UEFA said on Friday.
All the results from the I-League and ISL matches played on Saturday