Cumming scored 160 as Otago chased first-innings points in its four-day Plunket Shield match against Northern Districts in Whangarei yesterday.
It was Cumming's 18th first-class 100 and his 16th for Otago, leaving him just one behind the great left-hander.
Having overhauled Glenn Turner's total of 13 and Ken Rutherford's harvest of 14 earlier this year, Cumming now has Sutcliffe's record in his sights.
He missed out on an opportunity to add to his tally in Queenstown last week when he was undone for 82.
But he was not to be denied yesterday, whacking 27 fours in a marathon eight-hour stay at the crease.
He also shared in an outstanding 247-run stand with Darren Broom for the second wicket.
Broom played magnificently in his debut match, scoring 119 including 13 fours and two sixes.
The right-hander was selected to make his first-class debut a week earlier but was cut from the squad when his older brother Neil was dropped from the test squad and took his sibling's spot in the Otago team.
Chasing Northern Districts' first innings of 465 for nine declared, Otago was 486 for three at stumps last night, with Broom having departed caught by Kane Williamson off Graeme Aldridge, and Cumming joining him in the pavilion one run later as 341 for one became 342 for three.
That was only a minor blip, though, as Nathan McCullum and Greg Todd combined for a unbroken fourth-wicket stand of 144 to take Otago past the home side's total.
McCullum was the aggressor as he made 88 not out with 14 boundaries, while Todd was unbeaten on 51.
Left-arm spinner Bruce Martin got through a power of work for little reward, going wicketless for 54 overs but conceding just 101 runs during his marathon effort.
Northern Districts leads the competition by 12 points from Central Districts, which has conceded first-innings points in its ninth-round match against Auckland.
A draw in Whangarei will suit it fine, providing Central Districts does not perform a minor miracle and beat Auckland, as it will ensure it of the shield before the final round of matches starting on Monday.
Gareth Hopkins helped Auckland effectively bludgeon Central Districts out of contention yesterday.
Hopkins' 201 at Auckland's Colin Maiden Park was four runs short of the highest first-class score by a New Zealand wicketkeeper, recorded by Wellington stalwart Ervin McSweeney, whose unbeaten 205 also came against Central, in the 1988-89 season.
The 33-year-old was one of four Aucklanders to raise three figures as it declared at 635 for six, holding a first-innings lead of 366.
By stumps, Central had replied with 119 for three, still 247 behind and with virtually no hope of the outright win it needs to maintain pressure on Northern Districts.
In the other match yesterday, Wellington all-rounder James Franklin scored a fine century against Canterbury at Rangiora.
Released from the New Zealand squad after its one-day series against Australia, Franklin dined out on a helpful batting surface to score 162, his 10th first-class century.
It complemented an equally impressive 137 from opener Neal Parlane as Wellington sparked to life on the third day of the four-day fixture to post 447 in its second innings.
That left Canterbury requiring 306 for victory.
Wellington gave itself a realistic chance of securing a surprise result by reducing the home side to 45 for three by the close.
