Two of the pre-tournament favourites faced off at Bramall Lane, and it was Sweden, unbeaten so far in 2022, who took a 1-0 lead into the break after a low Kosovare Asllani cross found Jonna Andersson to slot a 36th-minute opener.
The Netherlands defeated the Swedes in the semi-finals of the 2019 World Cup, and they equalised in the 52nd minute when a fortunate deflection ran into the path of Roord who fired into the bottom-left corner.
Sari van Veenendaal in the Netherlands goal was forced off due to injury in the first half, and substitute goalkeeper Daphne van Domselaar made an important stop to deny Fridolina Rolfo a late winner.
Portugal came from two goals down to finish 2-2 with Switzerland in Leigh, in the day's other Group C game.
Switzerland had not won in six matches prior to their opener, including 4-0 and 7-0 thrashings from England and Germany respectively in their pre-tournament friendlies.
But their Euros campaign looked to be off to a flyer when a 25-yard shot from Coumba Sow and a powerful header from Rahel Kiwic put the Swiss 2-0 up after just five minutes.
Portugal had not had a shot on target by the time the referee blew the half-time whistle, and needed to improve if they were to find a way back.
They did exactly that and halved the deficit after 58 minutes when Diana Gomes met a corner from the left. Her initial header was saved, but she made no mistake with the rebound to make it 2-1.
The Portuguese then got themselves on level terms just seven minutes later, when a superb cross from Tatiana Pinto picked out Jessica Silva in the box, and she smartly side-footed into the bottom corner.
Both teams hit the woodwork late on in their pursuit for a winner, with Geraldine Reuteler and Telma Encarnacao the players going close.
In the next round of fixtures on Wednesday, the Netherlands play Portugal in Leigh as they look to get a foothold in Group C, while Switzerland and Sweden face off at Bramall Lane.
Miedema scored 14 goals in 22 Women's Super League appearances for runners-up Arsenal last season, a tally only bettered by Chelsea's Sam Kerr (20).
The 25-year-old, widely regarded as one of the best players in the women's game, has also netted an incredible 94 goals in 112 international appearances, making her the Netherlands' all-time leading scorer.
Miedema started her country's Euro 2022 opener on Saturday, a 1-1 draw with Sweden, but coronavirus will prevent her facing Portugal.
An update from the Oranje's Twitter account read: "Vivianne Miedema has unfortunately tested positive for COVID-19 and will therefore be in isolation for the next few days.
"When she no longer has any symptoms and tests negative, she can re-join the selection."
Miedema has scored 11 goals for the Netherlands since head coach Mark Parsons took charge last year – no Dutch player has more – and netted four times as the side won the last edition of the Women's Euros in 2017, including a brace in a 4-2 final win over Denmark.
It remains unclear whether the Arsenal forward will be back in action by the time the Netherlands finish their Group C campaign against Switzerland at Bramall Lane on Sunday.
The two pool favourites would have considered their meeting last week the toughest test of the first stage of the tournament, but Portugal and Switzerland were no pushovers on Wednesday.
Those two had played out their own entertaining draw, and Portugal repeated the two-goal comeback that rescued that point.
The Netherlands were coasting after a pair of headed goals through Damaris Egurrola and Stefanie van der Gragt, but the VAR spotted a foul on Diana Silva late in the first half that allowed Carole Costa to pull a goal back.
And Silva's header from Costa's cross had Portugal level, before the Oranje were again frustrated by a video review when Jill Roord's effort was struck off following a four-minute delay.
The defending European champions finally got their act together, though, and Danielle van de Donk arrowed into the top-right corner to earn a 3-2 Netherlands win.
It had been a similar story in the early game as Sweden beat Switzerland 2-1.
Sweden were the beneficiaries of a VAR review when Noelle Maritz went down easily and a penalty award was overturned, before Fridolina Rolfo steered the world's second-ranked side in front.
However, a fine Ramona Bachmann finish only 92 seconds later had Switzerland back on terms.
Teenage Sweden substitute Hanna Bennison restored the advantage with a 20-yard drive, yet her side were never in real comfort as they saw two late goals ruled out for offside.
Both teams won in their final group games, meaning they finished level on seven points and were separated by goal difference, having drawn when they faced each other earlier in the tournament.
Sweden thumped Portugal 5-0 while the Netherlands were 4-1 winners against Switzerland following a rush of late goals. Sweden finished with a plus-six goal difference, two better than the Netherlands achieved.
It means that five years on from triumphing on home soil, the Dutch must do it the hard way if they are to go deeper into this tournament, with France having caught the eye, particularly in their 5-1 rout of Italy.
France are certain to top Group D, while Sweden await the runner-up from that pool, with Italy, Iceland and Belgium all still in the hunt ahead of Monday's last round of matches.
Sweden, who sit second in the FIFA rankings, behind only the United States, showed why they should be taken seriously as contenders to win this tournament as they mauled Portugal in Leigh.
Filippa Angeldal scored twice for Sweden in the first half, and a Carole Costa own goal made it 3-0 at the break, before Kosovare Asllani's penalty and a late fifth from Stina Blackstenius completed the convincing victory. It matched Sweden's biggest victory at a European Championship.
Captain Asllani said: "We are feeling great. It was our goal to get through the group from the beginning. Today we had to win and we wanted to score as many goals as possible to win the game."
Quoted on UEFA's official website, she added: "We have a lot of respect for Portugal, they have developed a lot, but at the same time we just wanted to go all in and be as aggressive as possible in the last third."
The Netherlands were without star striker Vivianne Miedema for a second successive game after her COVID-19 positive test, but they still got the win against the Swiss at Bramall Lane.
It was a tight game until three late Dutch goals gave the scoreline a lopsided look. An own goal from Ana-Maria Crnogorcevic gave the Netherlands a 49th-minute lead, but Geraldine Reuteler levelled up four minutes later.
The teams remained locked until the 84th minute when Romee Leuchter netted the first of her late double, with Victoria Pelova also scoring in the dying moments.
