The in-form Dane made it five goals in his last four Premier League matches, netting in each half to assuage some of the growing frustration at Spurs, whose season had started to tail off amid a Champions League exit and worsening top-flight form.
Mauricio Pochettino's side – beaten 1-0 at Old Trafford at the weekend – led after 14 minutes, as Eriksen capped a fine passing move with an unstoppable left-footed strike beyond Marshall.
Having spurned opportunities to extend their lead before the interval, Spurs got their two-goal cushion in the 63rd minute after Kyle Walker's run and assist left Eriksen with a straightforward finish.
Hull, who are now winless in eight against Spurs, have not tasted victory on the road in the league since August and Mike Phelan's side remain firmly in the relegation battle after Wanyama's tap-in rubbed salt in the wounds.
Former Spurs midfielder Tom Huddlestone made a timely intervention to thwart a swift counter-attack early on as Eriksen looked to pick out the unmarked Dele Alli at the back post.
But Eriksen's next contribution proved far more telling. After Spurs had strung together 28 passes, Jan Vertonghen's lofted delivery over Ahmed Elmohamady set Danny Rose free down the left and his cross was driven home by Eriksen.
Hull were fortunate to get to the break only one behind, with Marshall producing an excellent save to deny Alli after the England star was left in space inside the area, while Vertonghen was too hesitant to capitalise on a presentable shooting opportunity soon after.
To their credit, the Tigers came out for the second half determined to make life difficult for their hosts and managed to stifle and frustrate Pochettino's side with some assiduous pressing.
And yet another ex-Spurs player almost levelled matters on the hour mark, with Jake Livermore's attempted side-footer from 12 yards kept out by an alert Hugo Lloris.
Hull's resistance was broken when Walker held off Andrew Robertson and rolled the ball across goal for Eriksen to provide a simple finish from a couple of yards.
When the home side won a free-kick 20 yards out 17 minutes from time, it was little surprise when Eriksen stepped up to take it. He struck it sweetly, forcing Marshall into a finger-tip save, but the ball came back off the inside of the goalkeeper's right-hand post and left Wanyama with an easy finish.
The result keeps Spurs firmly in touch with the top four, while Hull's search for a precious three points takes them to London again on Saturday, as they head to West Ham.
Key Opta stats:
- Spurs have scored in each of their last 16 league games at White Hart Lane, the longest current home scoring streak in the Premier League.
- Hull City have lost six consecutive Premier League away games for the first time since 2010.
- There were 30 passes leading to Eriksen's first goal for Tottenham, the most leading to a Premier League goal this season.
- Since his Premier League debut in September 2013, Eriksen has been involved in 55 goals in the competition (28 goals, 27 assists), with Eden Hazard the only midfielder with more (60 – while Mesut Ozil also has 55).