Kent 192 (Stevens 64, Stewart 63, Fuller 4-49) and 104 for 4 require a further 52 runs to beat Middlesex 161 (Stevens 4-44) and 186 (Henry 4-40, Podmore 3-35, Stevens 3-46)
A thrilling third day finish could be in prospect at Lord's where Division Two rivals Kent and Middlesex continue to cross swords in an action-packed Specsavers County Championship match.
After the loss of 19 wickets on day one, this low scoring clash continued with a further 15 falling on an enthralling second day that ended through bad light at 6.20pm with Kent on 104 for four - requiring another 52 runs with six, second innings wickets intact to secure their fourth successive championship win and strengthen their hold on a top-two place.
With a potential 39 overs remaining in the day, Kent looked to make an ultra-positive start to their run chase but paid the price with the loss of four cheap wickets.
Zak Crawley was superbly caught by Dawid Malan off Ethan Bamber, then an over later, Matt Henry - promoted to pinch hit at No3 - skewed his second ball to mid-off to gift his wicket to Steven Finn.
Sean Dickson and Joe Denly added 33 for the third wicket until Denly went leg before to James Fuller, then Dickson's stay for 32 ended when he prodded at the first ball of a new spell from Bamber to be caught low at second slip.
The umpires took the players off nine balls later for a 20-minute break for bad light, after which Daniel Bell-Drummond and Heino Kuhn emerged to add 50 runs in positive fashion before the gloom descended again.
Kent took a stranglehold on proceedings during the mid-session when New Zealand strike bowler Henry bagged four for 40 to inspire a Middlesex collapse that saw the hosts lose eight wickets for 88 runs.
In taking five victims in this game Henry, the championship's leading wicket-taker, took his season's tally to 66 at less than 15 apiece as Middlesex succumbed in 60.2 overs.
It was Kent's 42-year-old all-rounder Darren Stevens who started the home demise by breaking a useful opening stand worth 59 between Sam Morgan and Nick Gubbins.
Robson and Gubbins rode their luck under the floodlights as Henry and Harry Podmore beat the outside edge on numerous occasions. Yet, within 10 overs, Middlesex had wiped out the first innings deficit of 31 as the pair went on to record only their third 50-run first-wicket stand of the championship summer.
Stevens, fresh from signing a one-year contract extension to keep him at Kent for a 14th season, then struck at the double. Robson edged an away-singer to second slip then, four runs later, left-hander Max Holden fell leg before to an in-swinger that pitched on leg and middle to beat Holden's airy, leg-side flick.
Middlesex lost three wickets for one run in the space of 13 balls after lunch after resuming on their interval score of 98 for two. Gubbins, off balance and working across the line, departed lbw to Podmore, then Henry swung the very next delivery back in to end Dawid Malan's innings of 32.
Podmore's slower ball off-cutter, which turned into a dipping, low full-toss, was scooped straight to mid-wicket by Eoin Morgan and the procession continued when Martin Andersson, in crab-like defence, played inside the line to Podmore's in-ducker to be given lbw.
Stevie Eskinazi went in the same fashion to a shooting off-cutter from Stevens and Henry returned to polish things off with a 20-ball stint of three for seven. The slippery Kiwi got one to lift and leave Oli Rayner for a regulation catch at second slip then, in his next over, swung a full one away from Bamber for Sam Billings to snaffle a diving catch in front of slip.
Henry trapped Finn lbw for his 66th wicket of the championship campaign to leave Kent with a potential seven sessions of the match to secure their ninth win of the campaign.
The second day started with Kent completing their first innings. It lasted only another 11 deliveries as they added only three to their overnight score to miss out on a batting bonus point by eight runs.
Grant Stewart, the Australian-born all-rounder, was Kent's last man to go for a battling 63, bowled by Fuller when playing across the line of a very full delivery. Fuller, the pick of the home attack, finished with four for 49 as Kent secured a modest 31-run lead.